UNIVERSITY    OF    CALIFORNIA 


DEPARTMFNT   OF 


No. 


LQ       Q^ 

«   f 

<J       O 


i          | 

I 


TWENTIETH    CENTURY   TEXT-BOOKS 


A  TEXT-BOOK  OF 

ASTRONOMY 


BY 

GEORGE   C.   COMSTOCK 

DIRECTOR   OF    THE    WASHBURN    OBSERVATORY    AND 

PROFESSOR   OF    ASTRONOMY    IN    THE 

UNIVERSITY    OF    WISCONSIN 


NEW    YORK 

D.    APPLETON    AND    COMPANY 
1901 


COPYRIGHT,  1901 
BY   D.    APPLETON    AND    COMPANY 


EDUCATION 


PREFACE 


THE  present  work  is  not  a  compendium  of  astronomy 
or  an  outline  course  of  popular  reading  in  that  science.  It 
has  been  prepared  as  a  text-book,  and  the  author  has  pur- 
posely omitted  from  it  much  matter  interesting  as  well  as 
important  to  a  complete  view  of  the  science,  and  has  en- 
deavored to  concentrate  attention  upon  those  parts  of  the 
subject  that  possess  special  educational  value.  From  this 
point  of  view  matter  which  permits  of  experimental  treat- 
ment with  simple  apparatus  is  of  peculiar  value  and  is 
given  a  prominence  in  the  text  beyond  its  just  due  in  a 
well-balanced  exposition  of  the  elements  of  astronomy, 
while  topics,  such  as  the  results  of  spectrum  analysis, 
which  depend  upon  elaborate  apparatus,  are  in  the  experi- 
mental part  of  the  work  accorded  much  less  space  than 
their  intrinsic  importance  would  justify. 

Teacher  and  student  are  alike  urged  to  magnify  the 
observational  side  of  the  subject  and  to  strive  to  obtain  in 
their  work  the  maximum  degree  of  precision  of  which  their 
apparatus  is  capable.  The  instruments  required  are  few 
and  easily  obtained.  With  exception  of  a  watch  and  a  pro- 
tractor, all  of  the  apparatus  needed  may  be  built  by  any 
one  of  fair  mechanical  talent  who  will  follow  the  illustra- 
tions and  descriptions  of  the  text.  In  order  that  proper 
opportunity  for  observations  may  be  had,  the  study  should 
be  pursued  during  the  milder  portion  of  the  year,  between 
April  and  November  in  northern  latitudes,  using  clear 

V 

54. in  34 


vi  ASTRONOMY 

weather  for  a  direct  study  of  the  sky  and  cloudy  days  for 
book  work. 

The  illustrations  contained  in  the  present  work  are 
worthy  of  as  careful  study  as  is  the  text,  and  many  of 
them  are  intended  as  an  aid  to  experimental  work  and 
accurate  measurement,  e.  g.,  the  star  maps,  the  diagrams 
of  the  planetary  orbits,  pictures  of  the  moon,  sun,  etc.  If 
the  school  possesses  a  projection  lantern,  a  set  of  astro- 
nomical slides  to  be  used  in  connection  with  it  may  be 
made  of  great  advantage,  if  the  pictures  are  studied  as  an 
auxiliary  to  Nature.  Mere  display  and  scenic  effect  are  of 
little  value. 

A  brief  bibliography  of  popular  literature  upon  astron- 
omy may  be  found  at  the  end  of  this  book,  and  it  will  be 
well  if  at  least  a  part  of  these  works  can  be  placed  in  the 
school  library  and  systematically  used  for  supplementary 
reading.  An  added  interest  may  be  given  to  the  study  if 
one  or  more  of  the  popular  periodicals  which  deal  with 
astronomy  are  taken  regularly  by  the  school  and  kept 
within  easy  reach  of  the  students.  From  time  to  time 
the  teacher  may  well  assign  topics  treated  in  these  peri- 
odicals to  be  read  by  individual  students  and  presented 
to  the  class  in  the  form  of  an  essay. 

The  author  is  under  obligations  to  many  of  his  profes- 
sional friends  who  have  contributed  illustrative  matter  for 
his  text,  and  his  thanks  are  in  an  especial  manner  due  to 
the  editors  of  the  Astrophysical  Journal,  Astronomy  and 
Astrophysics,  and  Popular  Astronomy  for  permission  to 
reproduce  here  plates  which  have  appeared  in  those  peri- 
odicals, and  to  Dr.  Charles  Boynton,  who  has  kindly  read 
and  criticised  the  proofs. 

GEOKGE  C.  COMSTOCK. 

UNIVERSITY  OF  WISCONSIN,  February,  1901. 


CONTENTS 


CHAPTER  PAGE 

I. — DIFFERENT  KINDS  OF  MEASUREMENT     .        ....        .        1 

The  measurement  of  angles  and  time. 

II. — THE    STARS    AND   THEIR   DIURNAL    MOTION        .  .  .  10 

Finding  the  stars — Their  apparent  motion — Latitude — Direc- 
tion of  the  meridian — Sidereal  time — Definitions. 

III. — FlXED    AND   WANDERING    STARS        .  .  .  ...         29 

Apparent  motion  of  the  sun,  moon,  and  planets— Orbits  of  the 
planets — How  to  find  the  planets. 

IV. — CELESTIAL  MECHANICS    .        .        .....        .        .46 

Kepler's  laws — Newton's  laws  of  motion — The  law  of  gravita- 
tion— Orbital  motion — Perturbations — Masses  of  the  planets — 
Discovery  of  Neptune — The  tides. 

V. — THE   EARTH    AS   A   PLANET        .  .         •  .        .^          -.  .  .         70 

Size — Mass — Precession — The  warming  of  the  earth — The 
atmosphere — Twilight. 

VI. — THE    MEASUREMENT    OF   TIME  '.          -..".          .  .  .  .         86 

Solar  and  sidereal  time— Longitude— The  calendar— Chro- 
nology. 

VII. — ECLIPSES       .        .        .  ."....        .101 

Their  cause  and  nature — Eclipse  limits — Eclipse  maps — .Re- 
currence and  prediction  of  eclipses. 

. — INSTRUMENTS  AND  THE  PRINCIPLES  INVOLVED  IN  THEIR  USE    121 

The  clock — Radiant  energy — Mirrors  and  lenses — The  tele- 
scope—Camera—Spectroscope—Principles of  spectrum  analysis. 

IX.— THE  MOON      .        .        .        .        .        .       "...       .        .        .150 

Numerical  data — Phases— Motion — Librations — Lunar  topog- 
raphy— Physical  condition. 


viii  ASTRONOMY 

CHAPTER  PAGE 

X.— THE  SUN        .        _.-'••.        .        .      -,        .        *        ..       .     178 

Numerical  data— Chemical  nature — Temperature — Visible 
and  invisible  parts — Photosphere — Spots — Faculae — Chromo- 
sphere— Prominences — Corona — The  sun-spot  period — The  sun's 
rotation — Mechanical  theory  oi  the  sun. 

XI. — THE  PLANETS         .      ......        .        .        .     212 

Arrangement  of  the  solar  system — Bode's  law — Physical  con- 
dition of  the  planets — Jupiter — Saturn — Uranus  and  Neptune — 
Venus — Mercury — Mars — The  asteroids. 

XII. — COMETS  AND  METEORS    .        .        .     "  .        .        .        .        .    251 

Motion,  size,  and  mass  of  comets— Meteors — Their  number 
and  distribution — Meteor  showers — Relation  of  comets  and  me- 
teors— Periodic  comets — Comet  families  and  groups — Comet  tails 
— Physical  nature  of  comets — Collisions. 

XIII.— THE  FIXED  STARS  .        .        .  i     .        .        ...        .291 

Number  of  the  stars — Brightness — Distance — Proper  motion 
— Motion  in  line  of  sight — Double  stars — Variable  stars— New 
stars. 

XIV. — STARS  AND  NEBULA       .       V      *.        ;       .        .       .        .    330 

Stellar  colors  and  spectra — Classes  of  stars— Clusters — Nebu- 
lae— Their  spectra  and  physical  condition— The  Milky  Way — 
Construction  of  the  heavens — Extent  of  the  stellar  system. 

XV. — GROWTH  AND  DECAY      .        .        .        .        .        .       ...   .    .    358 

Logical  bases  and  limitations— Development  of  the  sun— The 
nebular  hypothesis — Tidal  friction — Roche's  limit — Development 
of  the  moon — Development  of  stars  and  nebulae — The  future. 

APPENDIX     :    .        .        .    "   .  .    v       .        .   .     ;        .        .'.      .    383 
INDEX 387 


LIST   OF    LITHOGRAPHIC   PLATES 

FACING  PAGE 

I. — Northern  Constellations         .  .  ....        .     124 

II. — Equatorial  Constellations       .  '.  ,  _.        .        ,        .        .     190 

III.— Map  of  Mars  .        .        ...  :  .        .        .       V     ..     246 

IV.— The  Pleiades    .        .    ~    .    ...  .  .        .        V        .        .     344 

Protractor •:'.'-.  In  pocket  at  back  of  book 


LIST   OF   FULL-PAGE   ILLUSTRATIONS 

FACING   PAGE 

A  Total  Solar  Eclipse      .         .         .    .."-'/    /       .         Frontispiece 

The  Harvard  College  Observatory,  Cambridge.  Mass. .        .        .  24 

Isaac  Xewton    .        ...        ...        ..      •*        .        .        .      •  .  46 

Galileo  Galilei  .        .        .        ."        ..',".        .        .        .  52 

The  Lick  Observatory,  Mount  Hamilton,  Cal.       .        ...  60 

The  Yerkes  Observatory,  Williams  Bay,  Wis 100 

The  Moon,  one  day  after  First  Quarter        .        .        .        ...  150 

William  Herschel      .        .        .        .....        .        .234 

Pierre  Simon  Laplace .        .        .  364 


ASTRONOMY 


CHAPTER  I 

DIFFERENT    KINDS    OF    MEASUREMENT 

1.  Accurate  measurement. — Accurate  measurement  is  the 
foundation  of  exact  science,  and  at  the  very  beginning  of 
his  study  in  astronomy  the  student  should  learn  something 
of  the  astronomer's  kind  of  measurement.  He  should  prac- 
tice measuring  the  stars  with  all  possible  care,  and  should 
seek  to  attain  the  most  accurate  results  of  which  his  instru- 
ments and  apparatus  are  capable.  The  ordinary  affairs  of 
life  furnish  abundant  illustration  of  some  of  these  measure- 
ments, such  as  finding  the  length  of  a  board  in  inches  or 
the  weight  of  a  load  of  coal  in  pounds  and  measurements 
of  both  length  and  weight  are  of  importance  in  astronomy, 
but  of  far  greater  astronomical  importance  than  these  are 
the  measurement  of  angles  and  the  measurement  of  time. 
A  kitchen  clock  or  a  cheap  watch  is  usually  thought  of  as 
a  machine  to  tell  the  "  time  of  day,"  but  it  may  be  used  to 
time  a  horse  or  a  bicycler  upon  a  race  course,  and  then  it 
becomes  an  instrument  to  measure  the  amount  of  time 
required  for  covering  the  length  of  the  course.  Astrono- 
mers use  a  clock  in  both  of  these  ways — to  tell  the  time  at 
which  something  happens  or  is  done,  and  to  measure  the 
amount  of  time  required  for  something ;  and  in  using  a 
clock  for  either  purpose  the  student  should  learn  to  take 
the  time  from  it  to  the  nearest  second  or  better,  if  it  has  a 

1 


ASTRONOMY 


seconds  hand,' 6r' to1 'a  small  fraction  of  a  minute,  by  esti- 
mating the  position  of  the  minute  hand  between  the  min- 
ute marks  on  the  dial.  Estimate  the  fraction  in  tenths  of 
a  minute,  not  in  halves  or  quarters. 

EXERCISE  1. — If  several  watches  are  available,  let  one 
person  tap  sharply  upon  a  desk  with  a  pencil  and  let  each 
of  the  others  note  the  time  by  the  minute  hand  to  the 
nearest  tenth  of  a  minute  'and  record  the  observations  as 
follows : 

2h.  44.5m.  First  tap.  2h.  46.4m.  1.9m. 
2h.  44.9m.  Second  tap.  2h.  46.7m.  1.8m. 
2h.  40.6m.  Third  tap.  2h.  48.6m.  2.0m. 

The  letters  h  and  m  are  used  as  abbreviations  for  hour  and 
minute.  The  first  and  second  columns  of  the  table  are  the 
record  made  by  one  student,  and  second  and  third  the  rec- 
ord made  by  another.  After  all  the  observations  have  been 
made  and  recorded  they  should  be  brought  together  and 
compared  by  taking  the  differences  between  the  times  re- 
corded for  each  tap,  as  is  shown  in  the  last  column.  This 
difference  shows  how  much  faster  one  watch  is  than  the 
other,  and  the  agreement  or  disagreement  of  these  differ- 
ences shows  the  degree  of  accuracy  of  the  observations. 
Keep  up  this  practice  until  tenths  of  a  minute  can  be  esti- 
mated with  fair  precision. 

2.  Angles  and  their  use. — An  angle  is  the  amount  of 
opening  or  difference  of  direction  between  two  lines  that 
cross  each  other.  At  twelve  o'clock  the  hour  and  minute 
hand  of  a  watch  point  in  the  same  direction  and  the  angle 
between  them  is  zero.  At  one  o'clock  the  minute  hand  is 
again  at  XII,  but  the  hour  hand  has  moved  to  I,  one 
twelfth  part  of  the  circumference  of  the  dial,  and  the  angle 
between  the  hands  is  one  twelfth  of  a  circumference.  It  is 
customary  to  imagine  the  circumference  of  a  dial  to  be  cut 
up  into  360  equal  parts — i.  e.,  each  minute  space  of  an  ordi- 
nary dial  to  be  subdivided  into  six  equal  parts,  each  of 


DIFFERENT  KINDS  OF  MEASUREMENT  3 

which  is  called  a  degree,  and  the  measurement  of  an  angle 
consists  in  finding  how  many  of  these  degrees  are  included 
in  the  opening  between  its  sides.  At  one  o'clock  the  angle 
between  the  hands  of  a  watch  is  thirty  degrees,  which  is 
usually  written  30°,  at  three  o'clock  it  is  90°,  at  six  o'clock 
180°,  etc. 

A  watch  may  be  used  to  measure  angles.  How?  But 
a  more  convenient  instrument  is  the  protractor,  which  is 
shown  in  Fig.  1,  applied  to  the  angle  ABC  and  showing 
that  A  BC  =  85°  as  near- 
ly as  the  protractor  scale 
can  be  read. 

The  student  should 
have  and  use  a  protrac- 
tor, such  as  is  fur- 
nished with  this  book, 
for  the  numerous  exer- 
cises which  are  to  follow. 

EXEECISE    2. — Draw  B  A 

neatly   a   triangle   with  FIG.  I.-A  protractor. 

sides  about  100  millimeters  long,  measure  each  of  its  an- 
gles and  take  their  sum.  No  matter  what  may  be  the 
shape  of  the  triangle,  this  sum  should  be  very  nearly  180° 
— exactly  180°  if  the  work  were  perfect — but  perfection 
can  seldom  be  attained  and  one  of  the  first  lessons  to 
be  learned  in  any  science  which  deals  with  measurement 
is,  that  however  careful  we  may  be  in  our  work  some 
minute  error  will  cling  to  it  and  our  results  can  be  only 
approximately  correct.  This,  however,  should  not  be 
taken  as  an  excuse  for  careless  work,  but  rather  as  a  stim- 
ulus to  extra  effort  in  order  that  the  unavoidable  errors 
may  be  made  as  small  as  possible.  In  the  present  case 
the  measured  angles  may  be  improved  a  little  by  adding 
(algebraically)  to  each  of  them  one  third  of  the  amount  by 
which  their  sum  falls  short  of  180°,  as  in  the  following 
example : 


4  ASTRONOMY 

Measured  angles.     Correction.      Corrected  angles. 

A 73^4  +0.1  73.°5 

B 49.3  +0.1  49.4 

C 57.0  +0.1  57.1 

Sum 179.7  180.0 

Defect +0.3 

This  process  is  in  very  common  use  among  astronomers, 
and  is  called  "  adjusting  "  the  observations. 

3.  Triangles. — The  instruments  used  by  astronomers  for 
the  measurement  of  angles  are  usually  provided  with  a 
telescope,  which  may  be  pointed  at  different  objects,  and 
with  a  scale,  like  that  of  the  protractor,  to  measure  the 
angle  through  which  the  telescope  is  turned  in  passing 
from  one  object  to  another.  In  this  way  it  is  possible  to 
measure  the  angle  between  lines  drawn  from  the  instru- 
ment to  two  distant  ob- 
jects, such  as  two  church 
steeples  or  the  sun  and 
moon,  and  this  is  usually 
called  the  angle  between 
the  objects.  By  meas- 
uring angles  in  this  way 
it  is  possible  to  deter- 
mine the  distance  to  an 

inaccessible  point,  as  shown  in  Fig.  2.  A  surveyor  at  A 
desires  to  know  the  distance  to  C\  on  the  opposite  side  of  a 
river  which  he  can  not  cross.  He  measures  with  a  tape  line 
along  his  own  side  of  the  stream  the  distance  A  B  —  100 
yards  and  then,  with  a  suitable  instrument,  measures  the 
angle  at  A  between  the  points  C  and  B,  and  the  angle  at 
B  between  <?and  A,  finding  BAC  =  73.4°,  A  B  C=  49.3°. 
To  determine  the  distance  A  C  he  draws  upon  paper  a  line 
100  millimeters  long,  and  marks  the  ends  a  and  b ;  with  a 
protractor  he  constructs  at  a  the  angle  ~b  a  c  =  73.4°,  and  at 
b  the  anglr  abc  =  49.3°,  and  marks  by  c  the  point  where 


DIFFERENT   KINDS  OF  MEASUREMENT  5 

the  two  lines  thus  drawn  meet.  With  the  millimeter  scale 
he  now  measures  the  distance  a  c  =  90.2  millimeters,  which 
determines  the  distance  A  C  across  the  river  to  be  90.2 
yards,  since  the  triangle  on  paper  has  been  made  simi- 
lar to  the  one  across  the  river,  and  millimeters  on  the  one 
correspond  to  yards  on  the  other.  What  is  the  proposition 
of  geometry  upon  which  this  depends?  The  measured 
distance  A  B  in  the  surveyor's  problem  is  called  a  base  line. 
EXERCISE  3. — With  a  foot  rule  and  a  protractor  meas- 
ure a  base  line  and  the  angles  necessary  to  determine  the 
length  of  the  schoolroom.  After  the  length  has  been  thus 
found,  measure  it  directly  with  the  foot  rule  and  compare 


FIG.  3.— Finding  the  moon's  distance  from  the  earth. 

the  measured  length  with  the  one  found  from  the  angles. 
If  any  part  of  the  work  has  been  carelessly  done,  the  stu- 
dent need  not  expect  the  results  to  agree. 

In  the  same  manner,  by  sighting  at  the  moon  from 
widely  different  parts  of  the  earth,  as  in  Fig.  3,  the  moon's 
distance  from  us  is  found  to  be  about  a  quarter  of  a  million 
miles.  What  is  the  base  line  in  this  case  ? 

4.  The  horizon — altitudes. — In  their  observations  astron- 
omers and  sailors  make  much  use  of  the  plane  of  the  hori- 
zon, and  practically  any  flat  and  level  surface,  such  as  that 
of  a  smooth  pond,  may  be  regarded  as  a  part  of  this  plane 
and  used  as  such.  A  very  common  observation  relating  to 


6  ASTRONOMY 

the  plane  of  the  horizon  is  called  "  taking  the  sun's  alti- 
tude," and  consists  in  measuring  the  angle  between  the 
sun's  rays  and  the  plane  of  the  horizon  upon  which  they 
fall.  This  angle  between  a  line  and  a  plane  appears  slightly 
different  from  the  angle  between  two  lines,  but  is  really  the 
same  thing,  since  it  means  the  angle  between  the  sun's  rays 
and  a  line  drawn  in  the  plane  of  the  horizon  toward  the 
point  directly  under  the  sun.  Compare  this  with  the  defi- 
nition given  in  the  geographies,  "  The  latitude  of  a  point 
on  the  earth's  surface  is  its  angular  distance  north  or  south 
of  the  equator,"  and  note  that  the  latitude  is  the  angle 
between  the  plane  of  the  equator  and  a  line  drawn  from 
the  earth's  center  to  the  given  point  on  its  surface. 

A  convenient  method  of  obtaining  a  part  of  the  plane 
of  the  horizon  for  use  in  observation  is  as  follows :  Place 
a  slate  or  a  pane  of  glass  upon  a  table  in  the  sunshine. 
Slightly  moisten  its  whole  surface  and  then  pour  a  little 
more  water  upon  it  near  the  center.  If  the  water  runs 
toward  one  side,  thrust  the  edge  of  a  thin  wooden  wedge 
under  this  side  and  block  it  up  until  the  water  shows  no 
tendency  to  run  one  way  rather  than  another ;  it  is  then 
level  and  a  part  of  the  plane  of  the  horizon.  Get  several 
wedges  ready  before  commencing  the  experiment.  After 
they  have  been  properly  placed,  drive  a  pin  or  tack  behind 
each  one  so  that  it  may  not  slip. 

5.  Taking  the  sun's  altitude.  EXERCISE  4. — Prepare  a 
piece  of  board  20  centimeters  or  more  square,  planed 
smooth  on  one  face  and  one  edge.  Drive  a  pin  perpen- 
dicularly into  the  face  of  the  board,  near  the  middle  of  the 
planed  edge.  Set  the  board  on  edge  on  the  horizon  plane 
and  turn  it  edgewise  toward  the  sun  so  that  a  shadow  of 
the  pin  is  cast  on  the  plane.  Stick  another  pin  into  the 
board,  near  its  upper  edge,  so  that  its  shadow  shall  fall 
exactly  upon  the  shadow  of  the  first  pin,  and  with  a  watch 
or  clock  observe  the  time  at  which  the  two  shadows  coin- 
cide. Without  lifting  the  board  from  the  plane,  turn  it 


DIFFERENT   KINDS  OF   MEASUREMENT  7 

around  so  that  the  opposite  edge  is  directed  toward  the  sun 
and  set  a  third  pin  just  as  the  second  one  was  placed,  and 
again  take  the  time.  Remove  the  pins  and  draw  fine  pencil 
lines,  connecting  the  holes,  as  shown  in  Fig.  4,  and  with 
the  protractor  measure  the  an- 
gle thus  marked.  The  student 
who  has  studied  elementary  ge- 
ometry should  be  able  to  dem- 
onstrate that  at  the  mean  of  the 
two  recorded  times  the  sun's  alti- 
tude was  equal  to  one  half  of  the 


angle  measured  in  the  figure.  FlG-  4. -Taking  the  sun's 

When    the    board    is   turned 

edgewise  toward  the  sun  so  that  its  shadow  is  as  thin  as 
possible,  rule  a  pencil  line  alongside  it  on  the  horizon  plane. 
The  angle  which  this  line  makes  with  a  line  pointing  due 
south  is  called  the  sun's  azimuth.  When  the  sun  is  south, 
its  azimuth  is  zero  ;  when  west,  it  is  90°  ;  when  east, 
270°,  etc. 

EXERCISE  5. — Let  a  number  of  different  students  take 
the  sun's  altitude  during  both  the  morning  and  afternoon 
session  and  note  the  time  of  each  observation,  to  the  near- 
est minute.  Verify  the  setting  of  the  plane  of  the  horizon 
from  time  to  time,  to  make  sure  that  no  change  has  occurred 
in  it. 

6.  Graphical  representations. — Make  a  graph  (drawing) 
of  all  the  observations,  similar  to  Fig.  5,  and  find  by  bisect- 
ing a  set  of  chords  g  to  #,  e  to  e^  d  to  d,  drawn  parallel  to 
B  B,  the  time  at  which  the  sun's  altitude  was  greatest.  In 
Fig.  5  we  see  from  the  intersection  of  M  M  with  B  B  that 
this  time  was  llh.  50m. 

The  method  of  graphs  which  is  here  introduced  is  of 
great  importance  in  physical  science,  and  the  student 
should  carefully  observe  in  Fig.  5  that  the  line  B  B  is  a 
scale  of  times,  which  may  be  made  long  or  short,  provided 
only  the  intervals  between  consecutive  hours  9  to  10,  10  to 


ASTRONOMY 


11,  11  to  12,  etc.,  are  equal.  The  distance  of  each  little 
circle  from  B  B  is  taken  proportional  to  the  sun's  altitude, 
and  may  be  upon  any  desired  scale — e.  g.,  a  millimeter  to 
a  degree — provided  the  same  scale  is  used  for  all  observa- 


d  ,-ff>—    —  -&-• — ~-^-.,d 


ST. 


'<£k 


B  9  10  11  -trl.2  1  SB 

FIG.  5. — A  graph  of  the  sun's  altitude. 

tions.  Each  circle  is  placed  accurately  over  that  part  of 
the  base  line  which  corresponds  to  the  time  at  which  the 
altitude  was  taken.  Square  ruled  paper  is  very  convenient, 
although  not  necessary,  for  such  diagrams.  It  is  especially 
to  be  noted  that  from  the  few  observations  which  are  rep- 
resented in  the  figure  a  smooth  curve  has  been  drawn 
through  the  circles  which  represent  the  sun's  altitude,  and 
this  curve  shows  the  altitude  of  the  sun  at  every  moment 
between  9  A.  M.  and  3  P.  M.  In  Fig.  5  the  sun's  altitude  at 
noon  was  57°.  What  was  it  at  half  past  two  ? 

7.  Diameter  of  a  distant  object. — By  sighting  over  a  pro- 
tractor, measure  the  angle  between  imaginary  lines  drawn 
from  it  to  the  opposite  sides  of  a  window.  Carry  the  pro- 
tractor farther  away  from  the  window  and  repeat  the  ex- 
periment, to  see  how  much  the  angle  changes.  The  angle 
thus  measured  is  called  "  the  angle  subtended  "  by  the  win- 
dow at  the  place  where  the  measurement  was  made.  If 
this  place  was  squarely  in  front  of  the  window  we  may 
draw  upon  paper  an  angle  equal  to  the  measured  one  and 
lay  off  from  the  vertex  along  its  sides  a  distance  propor- 
tional to  the  distance  of  the  window— e.  g.,  a  millimeter  for 


DIFFERENT  KINDS  OF   MEASUREMENT  9 

each  centimeter  of  real  distance.  If  a  cross  line  be  now 
drawn  connecting  the  points  thus  found,  its  length  will  be 
proportional  to  the  width  of  the  window,  and  the  width 
may  be  read  oil  to  scale,  a  centimeter  for  every  millimeter 
in  the  length  of  the  cross  line. 

The  astronomer  who  measures  with  an  appropriate  in- 
strument the  angle  subtended  by  the  moon  may  in  an 
entirely  similar  manner  find  the  moon's  diameter  and  has, 
in  fact,  found  it  to  be  2,163  miles.  Can  the  same  method 
be  used  to  find  the  diameter  of  the  sun  ?  A  planet  ?  The 
earth  ? 


. 


\J 


CHAPTEE  II 

THE   STARS   AND   THEIR  DIURNAL   MOTION 

8.  The  stars. — From  the  very  beginning  of  his  study  in 
astronomy,  and  as  frequently  as  possible,  the  student  should 
practice  watching  the  stars  by  night,  to  become  acquainted 
with  the  constellations  and  their  movements.     As  an  intro- 
duction to  this  study  he  may  face  toward  the  north,  and 
compare  the  stars  which  he  sees  in  that  part  of  the  sky  with 
the  map  of  the  northern  heavens,  given  on  Plate  I,  oppo- 
site  page  124.      Turn   the   map   around,  upside  down   if 
necessary,  until  the  stars  upon  it  match  the  brighter  ones 
in  the  sky.     Note  how  the  stars  are  grouped  in  such  con- 
spicuous constellations  as  the  Big  Dipper  (Ursa  Major),  the 
Little  Dipper  (Ursa  Minor),  and  Cassiopea.     These  three 
constellations  should  be  learned  so  that  they  can  be  recog- 
nized at  any  time. 

The  names  of  the  stars.—  Facing  the  star  map  is  a  key 
which  contains  the  names  of  the  more  important  constella- 
tions and  the  names  of  the  brighter  stars  in  their  constella- 
tions. These  names  are  for  the  most  part  a  Greek  letter 
prefixed  to  the  genitive  case  of  the  Latin  name  of  the  con- 
stellation. (See  the  Greek  alphabet  printed  at  the  end  of 
the  book.) 

9.  Magnitudes  of  the  stars. — Nearly  nineteen  centuries 
ago  St.  Paul  noted  that  "  one  star  diff ereth  from  another 
star  in  glory,"  and  no  more  apt  words  can  be  found  to  mark 
the  difference  of  brightness  which  the  stars  present.    Even 
prior  to  St.  Paul's  day  the  ancient  Greek  astronomers  had 
divided  the  stars  in  respect  of  brightness  into  six  groups, 

10 


THE  STARS  AND  THEIR  DIURNAL  MOTION          H 

which  the  modern  astronomers  still  use,  calling  each  group 
a  magnitude.  Thus  a  few  of  the  brightest  stars  are  said  to 
be  of  the  first  magnitude,  the  great  mass  of  faint  ones 
which  are  just  visible  to  the  unaided  eye  are  said  to  be  of 
the  sixth  magnitude,  and  intermediate  degrees  of  brilliancy 
are  represented  by  the  intermediate  magnitudes,  second, 
third,  fourth,  and  fifth.  The  student  must  not  be  misled 
by  the  word  magnitude.  It  has  no  reference  to  the  size  of 
the  stars,  but  only  to  their  brightness,  and  on  the  star  maps 
at  the  beginning  and  end  of  this  book  the  larger  and  smaller 
circles  by  which  the  stars  are  represented  indicate  only  the 
brightness  of  the  stars  according  to  the  system  of  magni- 
tudes. Following  the  indications  of  these  maps,  the  stu- 
dent should,  in  learning  the  principal  stars  and  constella- 
tions, learn  also  to  recognize  how  bright  is  a  star  of  the/ 
second,  fourth,  or  other  magnitude. 

10.  Observing  the  stars. — Find  on  the  map  and  in  the 
sky  the  stars  a  Ursae  Minoris,  a  Ursae  Majoris,  ft  Ursae  Ma- 
joris. What  geometrical  figure  will  fit  on  to  these  stars  ? 
In  addition  to  its  regular  name,  a  Ursae  Minoris  is  frequent- 
ly called  by  the  special  name  Polaris,  or  the  pole  star. 
Why  are  the  other  two  stars  called  "  the  Pointers  "  ?  What 
letter  of  the  alphabet  do  the  five  bright  stars  in  Cassiopea 


EXERCISE  6. — Stand  in  such  a  position  that  Polaris  is 
just  hidden  behind  the  corner  of  a  building  or  some  other 
vertical  line,  and  mark  upon  the  key  map  as  accurately  as 
possible  the  position  of  this  line  with  respect  to  the  other 
stars,  showing  which  stars  are  to  the  right  and  which  are 
to  the  left  of  it.  Kecord  the  time  (date,  hour,  and  minute) 
at  which  this  observation  was  made.  An  hour  or  two  later 
repeat  the  observation  at  the  same  place,  draw  the  line  and 
note  the  time,  and  you  will  find  that  the  line  last  drawn 
upon  the  map  does  not  agree  with  the  first  one.  The  stars 
have  changed  their  positions,  and  with  respect  to  the  verti- 
cal line  the  Pointers  are  now  in  a  different  direction  from 


12  ASTRONOMY 

Polaris.  Measure  with  a  protractor  the  angle  between  the 
two  lines  drawn  in  the  map,  and  use  this  angle  and  the 
recorded  times  of  the  observation  to  find  how  many  degrees 
per  hour  this  direction  is  changing.  It  should  be  about  15° 
per  hour.  If  the  observation  were  repeated  12  hours  after 
the  first  recorded  time,  what  would  be  the  position  of  the 
vertical  line  among  the  stars  ?  What  would  it  be  24  hours 
later  ?  A  week  later  ?  Kepeat  the  observation  on  the  next 
clear  night,  and  allowing  for  the  number  of  whole  revolu- 
tions made  by  the  stars  between  the  two  dates,  again  deter- 
mine from  the  time  interval  a  more  accurate  value  of  the 
rate  at  which  the  stars  move. 

The  motion  of  the  stars  which  the  student  has  here  de- 
tected is  called  their  u  diurnal "  motion.  What  is  the  sig- 
nificance of  the  word  diurnal  ? 

In  the  preceding  paragraph  there  is  introduced  a  method 
of  great  importance  in  astronomical  practice — i.  e.,  determin- 
ing something — in  this  case  the  rate  per  hour,  from  obser- 
vations separated  by  a  long  interval  of  time,  in  order  to  get 
a  more  accurate  value  than  could  be  found  from  a  short 
interval.  Why  is  it  more  accurate?  To  determine  the 
rate  at  which  the  planet  Mars  rotates  about  its  axis,  astron- 
omers use  observations  separated  by  an  interval  of  more 
than  200  years,  during  which  the  planet  made  more  than 
75,000  revolutions  upon  its  axis.  If  we  were  to  write  out 
in  algebraic  form  an  equation  for  determining  the  length 
of  one  revolution  of  Mars  about  its  axis,  the  large  number, 
75,000,  would  appear  in  the  equation  as  a  divisor,  and  in 
the  final  result  would  greatly  reduce  whatever  errors  existed 
in  the  observations  employed. 

Kepeat  Exercise  6  night  after  night,  and  note  whether 
the  stars  come  back  to  the  same  position  at  the  same  hour 
and  minute  every  night. 

11.  The  plumb-line  apparatus. — This  experiment,  and 
many  others,  may  be  conveniently  and  accurately  made 
with  no  other  apparatus  than  a  plumb  line,  and  a  device 


THE  STARS  AND  THEIR  DIURNAL  MOTION 


13 


for  sighting  past  it.  In  Figs.  6  and  7  there  is  shown  a 
simple  form  of  such  apparatus,  consisting  essentially  of  a 
board  which  rests  in  a  horizontal  position  upon  the  points 
of  three  screws  that  pass  through  it.  This  board  carries 


FIG.  6. 


The  plumb-line  apparatus. 


FIG.  7. 


a  small  box,  to  one  side  of  which  is  nailed  in  vertical  posi- 
tion another  board  5  or  6  feet  long  to  carry  the  plumb  line. 
This  consists  of  a  wire  or  fish  line  with  any  heavy  weight — 
e.  g.,  a  brick  or  flatiron — tied  to  its  lower  end  and  immersed 
in  a  vessel  of  water  placed  inside  the  box,  so  as  to  check 
any  swinging  motion  of  the  weight.  In  the  cover  of  the 
box  is  a  small  hole  through  which  the  wire  passes,  and  by 
turning  the  screws  in  the  baseboard  the  apparatus  may  be 
readily  leveled,  so  that  the  wire  shall  swing  freely  in  the 
center  of  the  hole  without  touching  the  cover  of  the  box. 


14  ASTRONOMY 

Guy  wires,  shown  in  the  figure,  are  applied  so  as  to  stiffen 
the  whole  apparatus.  A  board  with  a  screw  eye  at  each 
end  may  be  pivoted  to  the  upright,  as  in  Fig.  6,  for  measur- 
ing altitudes ;  or  to  the  box,  as  in  Fig.  7,  for  observing  the 
time  at  which  a  star  in  its  diurnal  motion  passes  through 
the  plane  determined  by  the  plumb  line  and  the  center  of 
the  screw  eye  through  which  the  observer  looks. 

The  whole  apparatus  may  be  constructed  by  any  person 
of  ordinary  mechanical  skill  at  a  very  small  cost,  and  it  or 
something  equivalent  should  be  provided  for  every  class  be- 
ginning observational  astronomy.  To  use  the  apparatus  for 
the  experiment  of  §  10,  it  should  be  leveled,  and  the  board 
with  the  screw  eyes,  attached  as  in  Fig.  7,  should  be  turned 
until  the  observer,  looking  through  the  screw  eye,  sees 
Polaris  exactly  behind  the  wire.  Use  a  bicycle  lamp  to 
illumine  the  wire  by  night.  The  apparatus  is  now  adjusted, 
and  the  observer  has  only  to  wait  for  the  stars  which  he 
desires  to  observe,  and  to  note  by  his  watch  the  time  at 
which  they  pass  behind  the  wire.  It  will  be  seen  that  the 
wire  takes  the  place  of  the  vertical  edge  of  the  building, 
and  that  the  board  with  the  screw  eyes  is  introduced  solely 
to  keep  the  observer  in  the  right  place  relative  to  the 
wire. 

12.  A  sidereal  clock. — Clocks  are  sometimes  so  made  and 
regulated  that  they  show  always  the  same  hour  and  minute 
when  the  stars  come  back  to  the  same  place,  and  such  a 
timepiece  is  called  a  sidereal  clock — i.  e.,  a  star-time  clock. 
Would  such  a  clock  gain  or  lose  in  comparison  with  an  ordi- 
nary watch  ?     Could  an  ordinary  watch  be  turned  into  a 
sidereal  watch  by  moving  the  regulator  ? 

13.  Photographing  the  stars.— EXERCISE  7. — For  any  stu- 
dent who  uses  a  camera.     Upon  some  clear  and  moonless 
night  point  the  camera,  properly  focused,  at  Polaris,  and 
expose  a  plate  for  three  or  four  hours.     Upon  developing 
the  plate  you  should  find  a  series  of  circular  trails  such  as 
are  shown  in  Fig.  8,  only  longer.     Each  one  of  these  is  pro- 


THE    STARS   AND  THEIR  DIURNAL   MOTION          15 

duced  by  a  star  moving  slowly  over  the  plate,  in  conse- 
quence of  its  changing  position  in  the  sky.  The  center 
indicated  by  these  curved  trails  is  called  the  pole  of  the 
heavens.  It  is  that  part  of  the  sky  toward  which  is  pointed 
the  axis  about  which  the  earth  rotates,  and  the  motion  of 
the  stars  around  the  center  is  only  an  apparent  motion  due 
to  the  rotation  of  the  earth  which  daily  carries  the  observer 
and  his  camera  around  this  axis  while  the  stars  stand  still, 
just  as  trees  and  fences  and  telegraph  poles  stand  still, 


FIG.  8.— Photographing  the  circumpolar  star?.— BARNARD. 

although  to  the  passenger  upon  a  railway  train  they  appear 
to  be  in  rapid  motion.  So  far  as  simple  observations  are 
concerned,  there  is  no  method  by  which  the  pupil  can  tell 
for  himself  that  the  motion  of  the  stars  is  an  apparent 
rather  than  a  real  one,  and,  following  the  custom  of  astron- 
omers, we  shall  habitually  speak  as  if  it  were  a  real  move- 
ment of  the  stars.  How  long  was  the  plate  exposed  in 
photographing  Fig.  8  ? 


16  ASTRONOMY 

14.  Finding  the  stars, — On  Plate  I,  opposite  page  124, 
the  pole  of  the  heavens  is  at  the  center  of  the  map,  near 
Polaris,  and  the  heavy  trail  near  the  center  of  Fig.  8  is 
made  by  Polaris.      See  if  you  can  identify  from  the  map 
any  of  the  stars  whose  trails  show  in  the  photograph.     The 
brighter  the  star  the  bolder  and  heavier  its  trail. 

Find  from  the  map  and  locate  in  the  sky  the  two  bright 
stars  Capella  and  Vega,  which  are  on  opposite  sides  of 
Polaris  and  nearly  equidistant  from  it.  Do  these  stars 
share  in  the  motion  around  the  pole  ?  Are  they  visible  on 
every  clear  night,  and  all  night  ? 

Observe  other  bright  stars  farther  from  Polaris  than 
are  Vega  and  Capella  and  note  their  movement.  Do  they 
move  like  the  sun  and  moon  ?  Do  they  rise  and  set  ? 

In  what  part  of  the  sky  do  the  stars  move  most  rapidly, 
near  the  pole  or  far  from  it  ? 

How  long  does  it  take  the  fastest  moving  stars  to  make 
the  circuit  of  the  sky  and  come  back  to  the  same  place  ? 
How  long  does  it  take  the  slow  stars  ? 

15.  Rising  and  setting  of  the  stars. — A  study  of  the  sky 
along  the  lines  indicated  in  these  questions  will  show  that 
there  is  a  considerable   part   of   it   surrounding  the  pole 
whose  stars  are  visible  on  every  clear  night.     The  same 
star  is  sometimes  high  in  the  sky,  sometimes  low,  some- 
times to  the  east  of  the  pole  and  at  other  times  west  of  it, 
but  is  always  above  the  horizon.     Such  stars  are  said  to 
be  circumpolar.     A  little  farther  from  the  pole  each  star, 
when  at  the  .lowest  point  of  its  circular  path,  dips  for  a 
time  below  the  horizon  and  is  lost  to  view,  and  the  farther 
it  is  away  from  the  pole  the  longer  does  it  remain  invisible, 
until,  in  the  case  of  stars  90°  away  from  the  pole,  we  find 
them  hidden  below  the   horizon   for  twelve  hours  out  of 
every  twenty-four  (see  Fig.   9).     The  sun  is  such  a  star, 
and  in  its  rising  and  setting  acts  precisely  as  does  every 
other  star  at  a  similar  distance  from  the  pole — only,  as  we 
shall  find  later,  each  star  keeps  always  at  (nearly)  the  same 


THE  STARS  AND   THEIR  DIURNAL  MOTION          17 

distance  from  the  pole,  while  the  sun  in  the  course  of  a 
year  changes  its  distance  from  the  pole  very  greatly,  and 
thus  changes  the  amount  of  time  it  spends  above  and  be- 


FIG.  9.  -Diurnal  motion  of  the  northern  constellations. 

low  the  horizon,  producing  in  this  way  the  long  days  of 
summer  and  the  short  ones  of  winter. 

How  much  time  do  stars  which  are  more  than  90°  from 
the  pole  spend  above  the  horizon  ? 

We  say  in  common  speech  that  the  sun  rises  in  the 
east,  but  this  is  strictly  true  only  at  the  time  when  it  is  90° 
distant  from  the  pole — i.  e.,  in  March  and  September.  At 
other  seasons  it  rises  north  or  south  of  east  according  as 
its  distance  from  the  pole  is  less  or  greater  than  90°,  and 
the  same  is  true  for  the  stars. 


18  ASTRONOMY 

16.  The  geography  of  the  sky, — Find  from  a  map  the 
latitude  and  longitude  of  your  schoolhouse.  Find  on  the 
map  the  place  whose  latitude  is  39°  and  longitude  77°  west 
of  the  meridian  of  Greenwich.  Is  there  any  other  place  in 
the  world  which  has  the  same  latitude  and  longitude  as 
your  schoolhouse  ? 

The  places  of  the  stars  in  the  sky  are  located  in  exactly 
the  manner  which  is  illustrated  by  these  geographical 
questions,  only  different  names  are  used.  Instead  of  lati- 
tude the  astronomer  says  declination,  in  place  of  longitude 
he  says  right  ascension,  in  place  of  meridian  he  says  hour 
circle,  but  he  means  by  these  new  names  the  same  ideas 
that  the  geographer  expresses  by  the  old  ones. 

Imagine  the  earth  swollen  up  until  it  fills  the  whole 
sky ;  the  earth's  equator  would  meet  the  sky  along  a  line 
(a  great  circle)  everywhere  90°  distant  from  the  pole,  and 
this  line  is  called  the  celestial  equator.  Trace  its  posi- 
tion along  the  middle  of  the  map  opposite  page  190  and 
notice  near  what  stars  it  runs.  Every  meridian  of  the 
swollen  earth  would  touch  the  sky  along  an  hour  circle — 
i.  e.,  a  great  circle  passing  through  the  pole  and  therefore 
perpendicular  to  the  equator.  Xote  that  in  the  map  one  of 
these  hour  circles  is  marked  0.  It  plays  the  same  part  in 
measuring  right  ascensions  as  does  the  meridian  of  Green- 
wich in  measuring  longitudes  ;  it  is  the  beginning,  from 
which  they  are  reckoned.  Xote  also,  at  the  extreme  left 
end  of  the  map,  the  four  bright  stars  in  the  form  of  a 
square,  one  side  of  which  is  parallel  and  close  to  the  hour 
circle,  which  is  marked  0.  This  is  familiarly  called  the 
Great  Square  in  Pegasus,  and  may  be  found  high  up  in  the 
southern  sky  whenever  the  Big  Dipper  lies  below  the  pole. 
Why  can  it  not  be  seen  when  Ursa  Major  is  above  the 
pole? 

Astronomers  use  the  right  ascensions  of  the  stars  not 
only  to  tell  in  what  part  of  the  sky  the  star  is  placed,  but 
also  in  time  reckonings,  to  regulate  their  sidereal  clocks,  and 


THE  STARS  AND  THEIR  DIURNAL  MOTION          19 

with  regard  to  this  use  they  find  it  convenient  to  express 
right  ascension  not  in  degrees  but  in  hours,  24  of  which 
fill  up  the  circuit  of  the  sky  and  each  of  which  is  equal  to 
15°  of  arc,  24  X  15  =  360.  The  right  ascension  of  Capella 
is  5h.  9m.  =  77.2°,  but  the  student  should  accustom  him- 
self to  using  it  in  hours  and  minutes  as  given  and  not  to 
change  it  into  degrees.  He  should  also  note  that  some 


FIG.  10.— From  a  photograph  of  the  Pleiades. 

stars  lie  on  the  side  of  the  celestial  equator  toward  Polaris, 
and  others  are  on  the  opposite  side,  so  that  the  astronomer 
has  to  distinguish  between  north  declinations  and  south 
declinations,  just  as  the  geographer  distinguishes  between 
north  latitudes  and  south  latitudes.  This  is  done  by  the 
use  of  the  +  and  —  signs,  a  4-  denoting  that  the  star  lies 
north  of  the  celestial  equator — i.  e.,  toward  Polaris. 

Find    on   Plate   II,   opposite    page   190,   the    Pleiades 


20  ASTRONOMY 

(Pleades),  E.  A.  =  3h.  42m.,  Dec.  =  +  23.8°.  Why  do 
they  not  show  on  Plate  I,  opposite  page  124?  In  what 
direction  are  they  from  Polaris  ?  This  is  one  of  the 
finest  star  clusters  in  the  sky,  but  it  needs  a  telescope  to 
bring  out  its  richness.  See  how  many  stars  you  can  count 
in  it  with  the  naked  eye,  and  afterward  examine  it  with 
an  opera  glass.  Compare  what  you  see  with  Fig.  10.  Find 
Antares,  E.  A.  =  16h.  23m.  Dec.  =  —  26.2°.  How  far  is 
it,  in  degrees,  from  the  pole  ?  Is  it  visible  in  your  sky  ? 
If  so,  what  is  its  color  ? 

Find  the  E.  A.  and  Dec.  of  a  Ursse  Majoris  ;  of  j3  Ursae 
Majoris ;  of  Polaris.  Find  the  Northern  Crown,  Corona 
Borealis,  E.  A.  =  15h.  30m.,  Dec.  =  -f  27.0°  ;  the  Beehive, 
Prmepe,  E.  A.  =  8h.  33m.,  Dec.  =  +  20.4°. 

These  should  be  looked  up,  not  only  on  the  map,  but 
also  in  the  sky. 

17.  Reference  lines  and  circles. — As  the  stars  move  across 
the  sky  in  their  diurnal  motion,  they  carry  the  framework 
of  hour  circles  and  equator  with  them,  so  that  the  right 
ascension  and  declination  of  each  star  remain  unchanged 
by  this  motion,  just  as  longitudes  and  latitudes  remain  un- 
changed by  the  earth's  rotation.  They  are  the  same  when 
a  star  is  rising  and  when  it  is  setting ;  when  it  is  above  the 
pole  and  when  it  is  below  it.  During  each  day  the  hour 
circle  of  every  star  in  the  heavens  passes  overhead,  and  at 
the  moment  when  any  particular  hour  circle  is  exactly 
overhead  all  the  stars  which  lie  upon  it  are  said  to  be  "  on 
the  meridian  " — i.  e.,  at  that  particular  moment  they  stand 
directly  over  the  observer's  geographical  meridian  and  upon 
the  corresponding  celestial  meridian. 

An  eye  placed  at  the  center  of  the  earth  and  capable  of 
looking  through  its  solid  substance  would  see  your  geograph- 
ical meridian  against  the  background  of  the  sky  exactly  cov- 
ering your  celestial  meridian  and  passing  from  one  pole 
through  your  zenith  to  the  other  pole.  In  Fig.  11  the  inner 
circle  represents  the  terrestrial  meridian  of  a  certain  place, 


THE  STARS  AND  THEIR  DIURNAL   MOTION 


21 


0,  as  seen  from  the  center  of  the  earth,  (7,  and  the  outer 
circle  represents  the  celestial  meridian  of  0  as  seen  from 
C,  only  we  must  imagine,  what  can  not  be  shown  on  the 
figure,  that  the  outer  circle  is  so  large  that  the  inner  one 
shrinks  to  a  mere  point  in 
comparison  with  it.  i$s#P  z 

represents  the  direction  IB. 
which  the  earth's  axis  passes 
through  the  center,  then  C  E 
at  right  angles  to  it  must 
be  the  direction  of  the  equa- 
tor which  we  suppose  to  be 
turned  edgewise  toward  us ; 
and  if  C  0  is  the  direction  of 
some  particular  point  on  the 
earth's  surface,  then  Z  di- 
rectly overhead  is  called  the 
zenith  of  that  point,  upon 

the  celestial  sphere.  The  line  C H  represents  a  direction 
parallel  to  the  horizon  plane  at  0,  and  HOP  is  the  angle 
which  the  axis  of  the  earth  makes  with  this  horizon  plane. 
The  arc  0  E  measures  the  latitude  of  0,  and  the  arc  Z  E 
measures  the  declination  of  Z,  and  since  by  elementary 
geometry  each  of  these  arcs  contains  the  same  number  of 
degrees  as  the  angle  E  O  Z,  we  have  the 

Theorem. — The   latitude    of  any  place  is  equal  to  the~~\ 
declination  of  its  zenith. 

Corollary. — Any  star  whose  declination  is  equal  to  your 
latitude  will  once  in  each  day  pass  through  your  zenith. 

18.  Latitude. — From  the  construction  of  the  figure 

Z  ECZ+  Z 
LHCP+  Z 


FIG.  11. — Reference  lines  and  circles. 


from  which  we  find  by  subtraction  and  transposition 

Z  ECZ=  Z  HCP 
and  this  gives  the  further 


22  ASTRONOMY 

Theorem. — The  latitude  of  any  place  is  equal  to  the 
elevation  of  the  pole  above  its  horizon  plane. 

""  An  observer  who  travels  north  or  south  over  the  earth 
changes  his  latitude,  and  therefore  changes  the  angle  be- 
tween his  horizon  plane  and  the  axis  of  the  earth.  What 
effect  will  this  have  upon  the  position  of  stars  in  his  sky  ? 
If  you  were  to  go  to  the  earth's  equator,  in  what  part  of 
the  sky  would  you  look  for  Polaris  ?  Can  Polaris  be  seen 
from  Australia  ?  From  South  America  ?  If  you  were  to 
go  from  Minnesota  to  Texas,  in  what 
respect  would  the  appearance  of 
stars  in  the  northern  sky  be  changed  ? 
How  would  the  appearance  of  stars 
in  the  southern  sky  be  changed  ? 

EXEKCISE  8. — Determine  your 
latitude  by  taking  the  altitude  of 
Polaris  when  it  is  at  some  one  of  the 
four  points  of  its  diurnal  path,  shown 

FIG.  12.-Diurnal  path  of        j       Fj        ^         ^         ifc    j         t    1   jt    j 
Polaris. 

said  to  be  at  upper  culmination,  and 

the  star  £  Ursae  Minoris  in  the  handle  of  the  Big  Dipper 
will  be  directly  below  it.  When  at  2  it  is  at  western  elon- 
gation, and  the  star  Castor  is  near  the  meridian.  When  it 
is  at  S  it  is  at  lower  culmination,  and  the  star  Spica  is  on 
the  meridian.  When  it  is  at  4  it  is  at  eastern  elongation, 
and  Altair  is  near  the  meridian.  All  of  these  stars  are 
conspicuous  ones,  which  the  student  should  find  upon  the 
map  and  learn  to  recognize  in  the  sky.  The  altitude  ob- 
served at  either  2  or  4  may  be  considered  equal  to  the  lati- 
tude of  the  place,  but  the  altitude  observed  when  Polaris 
is  at  the  positions  marked  1  and  8  must  be  corrected  for 
the  star's  distance  from  the  pole,  which  may  be  assumed 
equal  to  1.3°. 

The  plumb-line  apparatus  described  at  page  12  is  shown 
in  Fig.  6  slightly  modified,  so  as  to  adapt  it  to  measuring 
the  altitudes  of  stars.  Note  that  the  board  with  the  screw 


THE  STARS  AND  THEIR  DIURNAL  MOTION          23 

eye  at  one  end  has  been  transferred  from  the  box  to  the 
vertical  standard,  and  has  a  screw  eye  at  each  end.  When 
the  apparatus  has  been  properly  leveled,  so  that  the  plumb 
line  hangs  at  the  middle  of  the  hole  in  the  box  cover,  the 
board  is  to  be  pointed  at  the  star  by  sighting  through  the 
centers  of  the  two  screw  eyes,  and  a  pencil  line  is  to  be 
ruled  along  its  edge  upon  the  face  of  the  vertical  standard. 
After  this  has  been  done  turn  the  apparatus  halfway  around 
so  that  what  was  the  north  side  now  points  south,  level  it 
again  and  revolve  the  board  about  the  screw  which  holds  it 
to  the  vertical  standard,  until  the  screw  eyes  again  point  to 
the  star.  Rule  another  line  along  the  same  edge  of  the 
board  as  before  and  with  a  protractor  measure  the  angle 
between  these  lines.  Use  a  bicycle  lamp  if  you  need  artifi- 
cial light  for  your  work.  The  student  who  has  studied 
plane  geometry  should  be  able  to  prove  that  one  half  of  the 
angle  between  these  lines  is  equal  to  the  altitude  of  the 
star. 

After  you  have  determined  your  latitude  from  Polaris, 
compare  the  result  with  your  position  as  shown  upon  the 
best  map  available.  With  a  little  practice  and  considerable 
care  the  latitude  may  be  thus  determined  within  one  tenth 
of  a  degree,  which  is  equivalent  to  about  7  miles.  If 
you  go  10  miles  north  or  south  from  your  first  station  you 
should  find  the  pole  higher  up  or  lower  down  in  the  sky  by 
an  amount  which  can  be  measured  with  your  apparatus. 

19.  The  meridian  line. — To  establish  a  true  north  and 
south  line  upon  the  ground,  use  the  apparatus  as  described 
at  page  13,  and  when  Polaris  is  at  upper  or  lower  culmina- 
tion drive  into  the  ground  two  stakes  in  line  with  the  star 
and  the  plumb  line.  Such  a  meridian  line  is  of  great  con* 
venience  in  observing  the  stars  and  should  be  laid  out  and 
permanently  marked  in  some  convenient  open  space  from 
which,  if  possible,  all  parts  of  the  sky  are  visible.  June  and 
November  are  convenient  months  for  this  exercise,  since 
Polaris  then  comes  to  culmination  early  in  the  evening. 


24  ASTRONOMY 

20.  Time. — What  is  the  time  at  which  school  begins  in 
the  morning  ?  What  do  you  mean  by  "  the  time  "  ? 

The  sidereal  time  at  any  moment  is  the  right  ascension 
of  the  hour  circle  which  at  that  moment  coincides  with  the 
meridian.  When  the  hour  circle  passing  through  Sirius 
coincides  with  the  meridian,  the  sidereal  time  is  6h.  40m., 
since  that  is  the  right  ascension  of  Sirius,  and  in  astronom- 
ical language  Sirius  is  "  on  the  meridian "  at  6h.  40m. 
sidereal  time.  As  may  be  seen  from  the  map,  this  6h.  40m. 
is  the  right  ascension  of  Sirius,  and  if  a  clock  be  set  to  in- 
dicate 6h.  40m.  when  Sirius  crosses  the  meridian,  it  will 
show  sidereal  time.  If  the  clock  is  properly  regulated, 
every  other  star  in  the  heavens  will  come  to  the  meridian 
at  the  moment  when  the  time  shown  by  the  clock  is  equal 
to  the  right  ascension  of  the  star.  A  clock  properly  reg- 
ulated for  this  purpose  will  gain  about  four  minutes  per 
day  in  comparison  with  ordinary  clocks,  and  when  so  reg- 
ulated it  is  called  a  sidereal  clock.  The  student  should 
be  provided  with  such  a  clock  for  his  future  work,  but 
one  such  clock  will  serve  for  several  persons,  and  a  nut- 
meg clock  or  a  watch  of  the  cheapest  kind  is  quite  suffi- 
cient. 

EXERCISE  9. — Set  such  a  clock  to  sidereal  time  by 
means  of  the  transit  of  a  star  over  your  meridian.  For  this 
experiment  it  is  presupposed  that  a  meridian  line  has  been 
marked  out  on  the  ground  as  in  §  19,  and  the  simplest 
mode  of  performing  the  experiment  required  is  for  the 
observer,  having  chosen  a  suitable  star  in  the  southern  part 
of  the  sky,  to  place  his  eye  accurately  over  the  northern  end 
of  the  meridian  line  and  to  estimate  as  nearly  as  possible 
the  beginning  and  end  of  the  period  during  which  the  star 
appears  to  stand  exactly  above  the  southern  end  of  the 
line.  The  middle  of  this  period  may  be  taken  as  the  time 
at  which  the  star  crossed  the  meridian  and  at  this  moment 
the  sidereal  time  is  equal  to  the  right  ascension  of  the  star. 
The  difference  between  this  right  ascension  and  the  ob- 


THE  STARS  AND  THEIR  DIURNAL  MOTION          25 

served  middle  instant  is  the  error  of  the  clock  or  the 
amount  by  which  its  hands  must  be  set  back  or  forward  in 
order  to  indicate  true  sidereal  time. 

A  more  accurate  mode  of  performing  the  experiment 
consists  in  using  the  plumb-line  apparatus  carefully  ad- 
justed, as  in  Fig.  7,  so  that  the  line  joining  the  wire  to 
the  center  of  the  screw  eye  shall  be  parallel  to  the  meridian 
line.  Observe  the  time  by  the  clock  at  which  the  star  dis- 
appears behind  the  wire  as  seen  through  the  center  of  the 
screw  eye.  If  the  star  is  too  high  up  in  the  sky  for  con- 
venient observation,  place  a  mirror,  face  up,  just  north  of 
the  screw  eye  and  observe  star,  wire  and  screw  eye  by  re- 
flection in  it. 

The  numerical  right  ascension  of  the  observed  star  is 
needed  for  this  experiment,  and  it  may  be  measured  from 
the  star  map,  but  it  will  usually  be  best  to  observe  one  of 
the  stars  of  the  table  at  the  end  of  the  book,  and  to  obtain 
its  right  ascension  as  follows:  The  table  gives  the  right 
ascension  and  declination  of  each  star  as  they  were  at  the 
beginning  of  the  year  1900,  but  on  account  of  the  preces- 
sion (see  Chapter  V),  these  numbers  all  change  slowly  with 
the  lapse  of  time,  and  on  the  average  the  right  ascension  of 
each  star  of  the  table  must  be  increased  by  one  twentieth 
of  a  minute  for  each  year  after  1900 — i.  e.,  in  1910  the 
right  ascension  of  the  second  star  of  the  table  will  be 
Oh.  38.6m.  +  i#m.  —  Oh.  39.1m.  The  declinations  also 
change  slightly,  but  as  they  are  only  intended  to  help  in 
finding  the  star  on  the  star  maps,  their  change  may  be 
ignored. 

Having  set  the  clock  approximately  to  sidereal  time, 
observe  one  or  two  more  stars  in  the  same  way  as  above. 
The  difference  between  the  observed  time  and  the  right 
ascension,  if  any  is  found,  is  the  "  correction "  of  the 
clock.  This  correction  ought  not  to  exceed  a  minute  if  due 
care  has  been  taken  in  the  several  operations  prescribed. 
The  relation  of  the  clock  to  the  right  ascension  of  the  stars 
3 


26  ASTRONOMY 

is  expressed  in  the  following  equation,  with  which  the 
student  should  become  thoroughly  familiar  : 

A  =  T±  U 

T  stands  for  the  time  by  the  clock  at  which  the  star  crossed 
the  meridian.  A  is  the  right  ascension  of  the  star,  and  U 
is  the  correction  of  the  clock.  Use  the  -j-  sign  in  the  equa- 
tion whenever  the  clock  is  too  slow,  and  the  —  sign  when 
it  is  too  fast.  U  may  be  found  from  this  equation  when  A 
and  T  are  given,  or  A  may  be  found  when  T  and  U  are 
given.  It  is  in  this  way  that  astronomers  measure  the  right 
ascensions  of  the  stars  and  planets. 

Determine  U  from  each  star  you  have  observed,  and 
note  how  the  several  results  agree  one  with  another. 

21.  Definitions.— To  define  a  thing  or  an  idea  is  to  give 
a  description  sufficient  to  identify  it  and  distinguish  it 
from  every  other  possible  thing  or  idea.  If  a  definition 
does  not  come  up  to  this  standard  it  is  insufficient.  Any- 
thing beyond  this  requirement  is  certainly  useless  and 
probably  mischievous. 

Let  the  student  define  the  following  geographical  terms, 
and  let  him  also  criticise  the  definitions  offered  by  his  fel- 
low-students :  Equator,  poles,  meridian,  latitude,  longitude, 
north,  south,  east,  west. 

Compare  the  following  astronomical  definitions  with 
your  geographical  definitions,  and  criticise  them  in  the 
same  way.  If  you  are  not  able  to  improve  upon  them,  com- 
mit them  to  memory : 

The  Poles  of  the  heavens  are  those  points  in  the  sky 
toward  which  the  earth's  axis  points.  How  many  are 
there  ?  The  one  near  Polaris  is  called  the  north  pole. 

The  Celestial  Equator  is  a  great  circle  of  the  sky  distant 
90°  from  the  poles. 

The  Zenith  is  that  point  of  the  sky,  overhead,  toward 
which  a  plumb  line  points.  Why  is  the  word  overhead 
placed  in  the  definition  ?  Is  there  more  than  one  zenith  ? 


THE  STARS  AND  THEIR  DIURNAL  MOTION          27 

The  Horizon  is  a  great  circle  of  the  sky  90°  distant 
from  the  zenith. 

An  Hour  Circle  is  any  great  circle  of  the  sky  which 
passes  through  the  poles.  Every  star  has  its  own  hour 
circle. 

The  Meridian  is  that  hour  circle  which  passes  through 
the  zenith. 

A  Vertical  Circle  is  any  great  circle  which  passes 
through  the  zenith.  Is  the  meridian  a  vertical  circle  ? 

The  Declination  of  a  star  is  its  angular  distance  north 
or  south  of  the  celestial  equator. 

The  Right  Ascension  of  a  star  is  the  angle  included  be- 
tween its  hour  circle  and  the  hour  circle  of  a  certain  point 
on  the  equator  which  is  called  the  Vernal  Equinox.  From 
spherical  geometry  we  learn  that  this  angle  is  to  be  meas- 
ured either  at  the  pole  where  the  two  hour  circles  inter- 
sect, as  is  done  in  the  star  map  opposite  page  124,  or 
along  the  equator,  as  is  done  in  the  map  opposite  page 
190.  Eight  ascension  is  always  measured  from  the  ver- 
nal equinox  in  the  direction  opposite  to  that  in  which  the 
stars  appear  to  travel  in  their  diurnal  motion — i.  e.,  from 
west  toward  east. 

The  Altitude  of  a  star  is  its  angular  distance  above  the 
horizon. 

The  Azimuth  of  a  star  is  the  angle  between  the  meridian 
and  the  vertical  circle  passing  through  the  star.  A  star 
due  south  has  an  azimuth  of  0°.  Due  west,  90°.  Due 
north,  180°.  Due  east,  270°. 

What  is  the  azimuth  of  Polaris  in  degrees  ? 

What  is  the  azimuth  of  the  sun  at  sunrise  ?  At  sunset  ? 
At  noon  ?  Are  these  azimuths  the  same  on  different  days  ? 

The  Hour  Angle  of  a  star  is  the  angle  between  its  hour 
circle  and  the  meridian.  It  is  measured  from  the  meridian 
in  the  direction  in  which  the  stars  appear  to  travel  in  their 
diurnal  motion — i.  e.,  from  east  toward  west. 

What  is  the  hour  angle  of  the  sun  at  noon  ?    What  is 


28  ASTRONOMY 

the  hour  angle  of  Polaris  when  it  is  at  the  lowest  point  in 
its  daily  motion  ? 

22.  Exercises.— The  student  must  not  be  satisfied  with 
merely  learning  these  definitions.  He  must  learn  to  see 
these  points  and  lines  in  his  mind  as  if  they  were  visibly 
painted  upon  the  sky.  To  this  end  it  will  help  him  to  note 
that  the  poles,  the  zenith,  the  meridian,  the  horizon,  and 
the  equator  seem  to  stand  still  in  the  sky,  always  in  the 
same  place  with  respect  to  the  observer,  while  the  hour 
circles  and  the  vernal  equinox  move  with  the  stars  and 
keep  the  same  place  among  them.  Does  the  apparent  mo- 
tion of  a  star  change  its  declination  or  right  ascension  ? 
What  is  the  hour  angle  of  the  sun  when  it  has  the  greatest 
altitude  ?  "Will  your  answer  to  the  preceding  question  be 
true  for  a  star  ?  What  is  the  altitude  of  the  sun  after  sun- 
set ?  In  what  direction  is  the  north  pole  from  the  zenith  ? 
From  the  vernal  equinox  ?  Where  are  the  points  in  which 
the  meridian  and  equator  respectively  intersect  the  horizon  ? 


CHAPTER  III 

FIXED   AND   WANDERING   STARS 

23.  Star  maps, — Select  from  the  map  some  conspicuous 
constellation  that  will  be  conveniently  placed  for  observa- 
tion in  the  evening,  and  make  on  a  large  scale  a  copy  of  all 
the  stars  of  the  constellation  that  are  shown  upon  the  map. 
At  night  compare  this  copy  with  the  sky,  and  mark  in  upon 
your  paper  all  the  stars  of  the  constellation  which  are  not 
already  there.  Both  the  original  drawing  and  the  addi- 
tions made  to  it  by  night  should  be  carefully  done,  and  foi 
the  latter  purpose  what  is  called  the  method  of  allineations 
may  be  used  with  advantage — i.  e.,  the  new  star  is  in  line 
with  two  already  on  the  drawing  and  is  midway  between 
them,  or  it  makes  an  equilateral  triangle  with  two  otherss 
or  a  square  with  three  others,  etc. 

A  series  of  maps  of  the  more  prominent  constellations, 
such  as  Ursa  Major,  Cassiopea,  Pegasus,  Taurus,  Orion, 
Gemini,  Canis  Major,  Leo,  Corvus,  Bootes,  Virgo,  Hercules, 
Lyra,  Aquila,  Scorpius,  should  be  constructed  in  this  man- 
ner upon  a  uniform  scale  and  preserved  as  a  part  of  the 
student's  work.  Let  the  magnitude  of  the  stars  be  repre- 
sented on  the  maps  as  accurately  as  may  be,  and  note  the 
peculiarity  of  color  which  some  stars  present.  For  the 
most  part  their  color  is  a  very  pale  yellow,  but  occasionally 
one  may  be  found  of  a  decidedly  ruddy  hue — e.  g.,  Alde- 
baran  or  Antares.  Such  a  star  map,  not  quite  complete,  is 
shown  in  Fig.  13. 

So,  too,  a  sharp  eye  may  detect  that  some  stars  do  not 
remain  always  of  the  same  magnitude,  but  change  their 


30  ASTRONOMY 

brightness  from  night  to  night,  and  this  not  on  account  of 
cloud  or  mist  in  the  atmosphere,  but  from  something  in  the 


FIG.  13. — Star  map  of  the  region  about  Orion. 

star  itself.     Algol  is  one  of  the  most  conspicuous  of  these 
variable  stars,  as  they  are  called. 

24.  The  moon's  motion  among  the  stars. — Whenever  the 
moon  is  visible  note  its  position  among  the  stars  by  allinea- 
tions,  and  plot  it  on  the  key  map  opposite  page  190.  Keep 
a  record  of  the  day  and  hour  corresponding  to  each  such 
observation.  You  will  find,  if  the  work  is  correctly  done, 
that  the  positions  of  the  moon  all  fall  near  the  curved  line 
shown  on  the  map.  This  line  is  called  the  ecliptic. 


FIXED  AND  WANDERING  STARS  31 

After  several  such  observations  have  been  made  and 
plotted,  find  by  measurement  from  the  map  how  many 
degrees  per  day  the  moon  moves.  How  long  would  it  re- 
quire to  make  the  circuit  of  the  heavens  and  come  back  to 
the  starting  point  ? 

On  each  night  when  you  observe  the  moon,  make  on  a 
separate  piece  of  paper  a  drawing  of  it  about  10  centime- 
ters in  diameter  and  show  in  the  drawing  every  feature  of 
the  moon's  face  which  you  can  see — e.  g.,  the  shape  of  the 
illuminated  surface  (phase) ;  the  direction  among  the  stars 
of  the  line  joining  the  horns ;  any  spots  which  you  can  see 
upon  the  moon's  face,  etc.  An  opera  glass  will  prove  of 
great  assistance  in  this  work. 

Use  your  drawings  and  the  positions  of  the  moon  plot- 
ted upon  the  map  to  answer  the  following  questions  :  Does 
the  direction  of  the  line  joining  the  horns  have  any  special 
relation  to  the  ecliptic  ?  Does  the  amount  of  illuminated 
surface  of  the  moon  have  any  relation  to  the  moon's  angular 
distance  from  the  sun  ?  Does  it  have  any  relation  to  the 
time  at  which  the  moon  sets  ?  Do  the  spots  on  the  moon 
when  visible  remain  always  in  the  same  place  ?  Do  they 
come  and  go  ?  Do  they  change  their  position  with  relation 
to  each  other?  Can  you  determine  from  these  spots  that 
the  moon  rotates  about  an  axis,  as  the  earth  does?  In 
what  direction  does  its  axis  point  ?  How  long  does  it  take 
to  make  one  revolution  about  the  axis  ?  Is  there  any  day 
and  night  upon  the  moon  ? 

Each  of  these  questions  can  be  correctly  answered  from 
the  student's  own  observations  without  recourse  to  any 
book. 

25.  The  sun  and  its  motion. — Examine  the  face  of  the 
sun  through  a  smoked  glass  to  see  if  there  is  anything 
there  which  you  can  sketch. 

By  day  as  well  as  by  night  the  sky  is  studded  with  stars, 
only  they  can  not  be  seen  by  day  on  account  of  the  over- 
whelming glare  of  sunlight,  but  the  position  of  the  sun 


32  ASTRONOMY 

among  the  stars  may  be  found  quite  as  accurately  as  was 
that  of  the  moon,  by  observing  from  day  to  day  its  right 
ascension  and  declination,  and  this  should  be  practiced  at 
noon  on  clear  days  by  different  members  of  the  class. 

EXERCISE  10. — The  right  ascension  of  the  sun  may  be 
found  by  observing  with  the  sidereal  clock  the  time  of  its 
transit  over  the  meridian.  Use  the  equation  in  §  20,  and 
substitute  in  place  of  U  the  value  of  the  clock  correction 
found  from  observations  of  stars  on  a  preceding  or  fol- 
lowing night.  If  the  clock  gains  or  loses  with  respect  to 
sidereal  time,  take  this  into  account  in  the  value  of  U. 

EXEECISE  11. — To  determine  the  sun's  decimation, 
measure  its  altitude  at  the  time  it  crosses  the  meridian. 
Use  either  the  method  of  Exercise  4,  or  that  used  with 
Polaris  in  Exercise  8.  The  student  should  be  able  to  show 
from  Fig.  11  that  the  declination  is  equal  to  the  sum  of 
the  altitude  and  the  latitude  of  the  place  diminished  by 
90°,  or  in  an  equation 

Declination  =  Altitude  -j-  Latitude  —  90°. 

If  the  declination  as  found  from  this  equation  is  a  negative 
number  it  indicates  that  the  sun  is  on  the  south  side  of  the 
equator. 

The  right  ascension  and  declination  of  the  sun  as  ob- 
served on  each  day  should  be  plotted  on  the  map  and  the 
date,  written  opposite  it.  If  the  work  has  been  correctly 
done,  the  plotted  points  should  fall  upon  the  curved  line 
(ecliptic)  which  runs  lengthwise  of  the  map.  This  line,  in 
fact,  represents  the  sun's  path  among  the  stars. 

Note  that  the  hours  of  right  ascension  increase  from  0 
up  to  24,  while  the  numbers  on  the  clock  dial  go  only  from 
0  to  12,  and  then  repeat  0  to  12  again  during  the  same 
day.  When  the  sidereal  time  is  13  hours,  14  hours,  etc., 
the  clock  will  indicate  1  hour,  2  hours,  etc.,  and  12  hours 
must  then  be  added  to  the  time  shown  on  the  dial. 

If  observations  of  the  sun's  right  ascension  and  declina- 


FIXED  AND  WANDERING  STARS  33 

tion  are  made  in  the  latter  part  of  either  March  or  Septem- 
ber the  student  will  find  that  the  sun  crosses  the  equator 
at  these  times,  and  he  should  determine  from  his  observa- 
tions, as  accurately  as  possible,  the  date  and  hour  of  this 
crossing  and  the  point  on  the  equator  at  which  the  sun 
crosses  it.  These  points  are  called  the  equinoxes,  Vernal 
Equinox  and  Autumnal  Equinox  for  the  spring  and  autumn 
crossings  respectively,  and  the  student  will  recall  that  the 
vernal  equinox  is  the  point  from  which  right  ascensions 
are  measured.  Its  position  among  the  stars  is  found  by 
astronomers  from  observations  like  those  above  described, 
only  made  with  much  more  elaborate  apparatus. 

Similar  observations  made  in  June  and  December  show 
that  the  sun's  midday  altitude  is  about  47°  greater  in  sum- 
mer than  in  winter.  They  show  also  that  the  sun  is  as  far 
north  of  the  equator  in  June  as  he  is  south  of  it  in  Decem- 
ber, from  which  it  is  easily  inferred  that  his  path,  the 
ecliptic,  is  inclined  to  the  equator  at  an  angle  of  23°. 5,  one 
half  of  47°.  This  angle  is  called  the  obliquity  of  the  eclip- 
tic. The  student  may  recall  that  in  the  geographies  the 
torrid  zone  is  said  to  extend  23°. 5  on  either  side  of  the 
earth's  equator.  Is  there  any  connection  between  these 
limits  and  the  obliquity  of  the  ecliptic  ?  Would  it  be  cor- 
rect to  define  the  torrid  zone  as  that  part  of  the  earth's 
surface  within  which  the  sun  may  at  some  season  of  the 
year  pass  through  the  zenith  ? 

EXERCISE  12. — After  a  half  dozen  observations  of  the 
sun  have  been  plotted  upon  the  map,  find  by  measurement 
the  rate,  in  degrees  per  day,  at  which  the  sun  moves  along 
the  ecliptic.  How  many  days  will  be  required  for  it  to 
move  completely  around  the  ecliptic  from  vernal  equinox 
back  to  vernal  equinox  again  ?  Accurate  observations  with 
the  elaborate  apparatus  used  by  professional  astronomers 
show  that  this  period,  which  is  called  a  tropical  year,  is  365 
days  5  hours  48  minutes  46  seconds.  Is  this  the  same  as 
the  ordinary  year  of  our  calendars  ? 


34:  ASTRONOMY 

26.  The  planets. — Any  one  who  has  watched  the  sky  and 
who  has  made  the  drawings  prescribed  in  this  chapter  can 
hardly  fail  to  have  fonnd  in  the  course  of  his  observations 
some  bright  stars  not  set  down  on  the  printed  star  maps, 
and  to  have  fonnd  also  that  these  stars  do  not  remain  fixed 
in  position  among  their  fellows,  bnt  wander  about  from 
one  constellation  to  another.  Observe  the  motion  of  one 
of  these  planets  from  night  to  night  and  plot  its  posi- 
tions on  the  star  map,  precisely  as  was  done  for  the  moon. 
What  kind  of  path  does  it  follow  ? 

Both  the  ancient  Greeks  and  the  modern  Germans  have 
called  these  bodies  wandering  stars,  and  in  English  we  name 
them  planets,  which  is  simply  the  Greek  word  for  wanderer, 
bent  to  our  use.  Besides  the  sun  and  moon  there  are  in 
the  heavens  five  planets  easily  visible  to  the  naked  eye  and, 
as  we  shall  see  later,  a  great  number  of  smaller  ones  visible 
only  in  the  telescope.  More  than  2,000  years  ago  astron- 
omers began  observing  the  motion  of  sun,  moon,  and 
planets  among  the  stars,  and  endeavored  to  account  for 
these  motions  by  the  theory  that  each  wandering  star 
moved  in  an  orbit  about  the  earth.  Classical  and  mediaeval 
literature  are  permeated  with  this  idea,  which  was  displaced 
only  after  a  long  struggle  begun  by  Copernicus  (1543  A.  D.), 
who  taught  that  the  moon  alone  of  these  bodies  revolves 
about  the  earth,  while  the  earth  and  the  other  planets  re- 
volve around  the  sun.  The  ecliptic  is  the  intersection  of 
the  plane  of  the  earth's  orbit  with  the  sky,  and  the  sun  ap- 
pears to  move  along  the  ecliptic  because,  as  the  earth  moves 
around  its  orbit,  the  sun  is  always  seen  projected  against 
the  opposite  side  of  it.  The  moon  and  planets  all  appear 
to  move  near  the  ecliptic  because  the  planes  of  their  orbits 
nearly  coincide  with  the  plane  of  the  earth's  orbit,  and  a 
narrow  strip  on  either  side  of  the  ecliptic,  following  its 
course  completely  around  the  sky,  is  called  the  zodiac,  n 
word  which  may  be  regarded  as  the  name  of  a  narrow  street 
(16°  wide)  within  which  all  the  wanderings  of  the  visible 


FIXED  AND   WANDERING  STARS  35 

planets  are  confined  and  outside  of  which  they  never  ven- 
ture. Indeed,  Mars  is  the  only  planet  which  ever  approaches 
the  edge  of  the  street,  the  others  traveling  near  the  middle 
of  the  road. 

27.  A  typical  case  of  planetary  motion. — The  Copernican 
theory,  enormously  extended  and  developed  through  the 

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FIG.  14.— The  apparent  motion  of  a  planet. 

Newtonian  law  of  gravitation  (see  Chapter  IV),  has  com- 
pletely supplanted  the  older  Ptolemaic  doctrine,  and  an 
illustration  of  the  simple  manner  in  which  it  accounts  for 
the  apparently  complicated  motions  of  a  planet  among  the 
stars  is  found  in  Figs.  14  and  15,  the  first  of  which  repre- 
sents the  apparent  motion  of  the  planet  Mars  through  the 
constellations  Aries  and  Pisces  during  the  latter  part  of  the 


36  ASTRONOMY 

year  1894,  while  the  second  shows  the  true  motions  of  Mars 
and  the  earth  in  their  orbits  about  the  sun  during  the  same 
period.  The  straight  line  in  Fig.  14,  with  cross  ruling  upon 
it,  is  a  part  of  the  ecliptic,  and  the  numbers  placed  opposite 
it  represent  the  distance,  in  degrees,  from  the  vernal  equi- 
nox. In  Fig.  15  the  straight  line  represents  the  direction 
from  the  sun  toward  the  vernal  equinox,  and  the  angle 
which  this  line  makes  with  the  line  joining  earth  and  sun  is 
called  the  earth's  longitude.  The  imaginary  line  joining 
the  earth  and  sun  is  called  the  earth's  radius  vector,  and 
the  pupil  should  note  that  the  longitude  and  length  of  the 
radius  vector  taken  together  show  the  direction  and  dis- 
tance of  the  earth  from  the  sun — i.  e.,  they  fix  the  relative 
positions  of  the  two  bodies.  The  same  is  nearly  true  for 
Mars  and  would  be  wholly  true  if  the  orbit  of  Mars  lay  in 
the  same  plane  with  that  of  the  earth.  How  does  Fig.  14 
show  that  the  orbit  of  Mars  does  not  lie  exactly  in  the  same 
plane  with  the  orbit  of  the  earth  ? 

EXERCISE  13. — Find  from  Fig.  15  what  ought  to  have 
been  the  apparent  course  of  Mars  among  the  stars  during 
the  period  shown  in  the  two  figures,  and  compare  what  you 
find  with  Fig.  14.  The  apparent  position  of  Mars  among 
the  stars  is  merely  its  direction  from  the  earth,  and  this 
direction  is  represented  in  Fig.  14  by  the  distance  of  the 
planet  from  the  ecliptic  and  by  its  longitude. 

The  longitude  of  Mars  for  each  date  can  be  found  from 
Fig.  15  by  measuring  the  angle  between  the  straight  line 
S  V  and  the  line  drawn  from  the  earth  to  Mars.  Thus  for 
October  12th  we  may  find  with  the  protractor  that  the  angle 
between  the  line  S  V  and  the  line  joining  the  earth  to  Mars 
is  a  4ittle  more  than  30°,  and  in  Fig.  14  the  position  of 
Mars  for  this  date  is  shown  nearly  opposite  the  cross  line 
corresponding  to  30°  on  the  ecliptic.  Just  how  far  below 
the  ecliptic  this  position  of  Mars  should  fall  can  not  be 
told  from  Fig.  15,  which  from  necessity  is  constructed  as  if 
the  orbits  of  Mars  and  the  earth  lay  in  the  same  plane,  and 


FIXED  AND  WANDERING  STARS  37 

Mars  in  this  case  would  always  appear  to  stand  exactly  on 
the  ecliptic  and  to  oscillate  back  and  forth  as  shown  in  Fig. 
14,  but  without  the  up-and-down  motion  there  shown.  In 
this  way  plot  in  Fig.  14  the  longitudes  of  Mars  as  seen  from 


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FIG.  15.— The  real  motion  of  a  planet. 

the  earth  for  other  dates  and  observe  how  the  forward  mo- 
tion of  the  two  planets  in  their  orbits  accounts  for  the  appar- 
ently capricious  motion  of  Mars  to  and  fro  among  the  stars. 


38 


ASTRONOMY 


28.  The  orbits  of  the  planets.— Each  planet,  great  or 
small,  moves  in  its  own  appropriate  orbit  about  the  sun, 
and  the  exact  determination  of  these  orbits,  their  sizes, 
shapes,  positions,  etc.,  has  been  one  of  the  great  problems 


FIG.  16.— The  orbits  of  Jupiter  and  Saturn. 

of  astronomy  for  more  than  2,000  years,  in  which  succes- 
sive generations  of  astronomers  have  striven  to  push  to  a 
still  higher  degree  of  accuracy  the  knowledge  attained  by 
their  predecessors.  Without  attempting  to  enter  into  the 
details  of  this  problem  we  may  say,  generally,  that  every 


FIXED  AND  WANDERING  STARS  39 

planet  moves  in  a  plane  passing  through  the  sun,  and  for 
the  six  planets  visible  to  the  naked  eye  these  planes  nearly 
coincide,  so  that  the  six  orbits  may  all  be  shown  without 
much  error  as  lying  in  the  flat  surface  of  one  map.  It  is, 
however,  more  convenient  to  use  two  maps,  such  as  Figs.  16 
and  17,  one  of  which  shows  the  group  of  planets,  Mercury, 
Venus,  the  earth,  and  Mars,  which  are  near  the  sun,  and 
on  this  account  are  sometimes  called  the  inner  planets, 
while  the  other  shows  the  more  distant  planets,  Jupiter  and 
Saturn,  together  with  the  earth,  whose  orbit  is  thus  made 
to  serve  as  a  connecting  link  between  the  two  diagrams. 
These  diagrams  are  accurately  drawn  to  scale,  and  are  in- 
tended to  be  used  by  the  student  for  accurate  measure- 
ment in  connection  with  the  exercises  and  problems  which 
follow. 

In  addition  to  the  six  planets  shown  in  the  figures  the 
solar  system  contains  two  large  planets  and  several  hundred 
small  ones,  for  the  most  part  invisible  to  the  naked  eye, 
which  are  omitted  in  order  to  avoid  confusing  the  dia- 
grams. 

29.  Jupiter  and  Saturn. — In  Fig.  16  the  sun  at  the  center 
is  encircled  by  the  orbits  of  the  three  planets,  and  inclosing 
all  of  these  is  a  circular  border  showing  the  directions  from 
the  sun  of  the  constellations  which  lie  along  the  zodiac. 
The  student  must  note  carefully  that  it  is  only  the  direc- 
tions of  these  constellations  which  are  correctly  shown,  and 
that  in  order  to  show  them  at  all  they  have  been  placed 
very  much  too  close  to  the  sun.  The  cross  lines  extending 
from  the  orbit  of  the  earth  toward  the  sun  with  Eoman 
numerals  opposite  them  show  the  positions  of  the  earth  in 
its  orbit  on  the  first  day  of  January  (7),  first  day  of  Feb- 
ruary (//),  etc.,  and  the  similar  lines  attached  to  the  orbits 
of  Jupiter  and  Saturn  with  Arabic  numerals  show  the  posi- 
tions of  those  planets  on  the  first  day  of  January  of  each 
year  indicated,  so  that  the  figure  serves  to  show  not  only 
the  orbits  of  the  planets,  but  their  actual  positions  in  their 


4:0 


ASTKONOMY 


orbits  for  something  more  than  the  first  decade  of  the  twen- 
tieth century. 

The  line  drawn  from  the  sun  toward  the  right  of  the 
figure  shows  the  direction  to  the  vernal  equinox.  It  forms 
one  side  of  the  angle  which  measures  a  planet's  longitude. 


FIG.  17.— The  orbits  of  the  inner  planets. 

EXERCISE  14. — Measure  with  your  protractor  the  longi- 
tude of  the  earth  on  January  1st.  Is  this  longitude  the 
same  in  all  years  ?  Measure  the  longitude  of  Jupiter  on 
January  1,  1900;  on  July  1,  1900;  on  September  25,  1906. 


FIXED  AND   WANDERING  STARS  41 

Draw  neatly  on  the  map  a  pencil  line  connecting  the 
position  of  the  earth  for  January  1,  1900,  with  the  position 
of  Jupiter  for  the  same  date,  and  produce  the  line  beyond 
Jupiter  until  it  meets  the  circle  of  the  constellations.  This 
line  represents  the  direction  of  Jupiter  from  the  earth,  and 
points  toward  the  constellation  in  which  the  planet  appears 
at  that  date.  But  this  representation  of  the  place  of  Jupi- 
ter in  the  sky  is  not  a  very  accurate  one,  since  on  the  scale 
of  the  diagram  the  stars  are  in  fact  more  than  100,000  times 
as  far  off  as  they  are  shown  in  the  figure,  and  the  pencil 
mark  does  not  meet  the  line  of  constellations  at  the  same 
intersection  it  would  have  if  this  line  were  pushed  back 
to  its  true  position.  To  remedy  this  defect  we  must  draw 
another  line  from  the  sun  parallel  to  the  one  first  drawn, 
and  its  intersection  with  the  constellations  will  give  very 
approximately  the  true  position  of  Jupiter  in  the  sky. 

EXERCISE  15. — Find  the  present  positions  of  Jupiter 
and  Saturn,  and  look  them  up  in  the  sky  by  means  of  your 
star  maps.  The  planets  will  appear  in  the  indicated  con- 
stellations as  very  bright  stars  not  shown  on  the  map. 

Which  of  the  planets,  Jupiter  and  Saturn,  changes  its 
direction  from  the  sun  more  rapidly  ?  Which  travels  the 
greater  number  of  miles  per  day  ?  When  will  Jupiter  and 
Saturn  be  in  the  same  constellation  ?  Does  the  earth  move 
faster  or  slower  than  Jupiter  ? 

The  distance  of  Jupiter  or  Saturn  from  the  earth  at  any 
time  may  be  readily  obtained  from  the  figure.  Thus,  by 
direct  measurement  with  the  millimeter  scale  we  find  for 
January  1, 1900,  the  distance  of  Jupiter  from  the  earth  is  6.1 
times  the  distance  of  the  sun  from  the  earth,  and  this  may 
be  turned  into  miles  by  multiplying  it  by  93,000,000,  which 
is  approximately  the  distance  of  the  sun  from  the  earth. 
For  most  purposes  it  is  quite  as  well  to  dispense  with  this 
multiplication  and  call  the  distance  6.1  astronomical  units, 
remembering  that  the  astronomical  unit  is  the  distance  of 
the  sun  from  the  earth. 
4 


42  ASTRONOMY 

EXEKCISE  16. — What  is  Jupiter's  distance  from  the  earth 
at  its  nearest  approach  ?  What  is  the  greatest  distance  it 
ever  attains?  Is  Jupiter's  least  distance  from  the  earth 
greater  or  less  than  its  least  distance  from  Saturn  ? 

On  what  day  in  the  year  1906  will  the  earth  be  on 
line  between  Jupiter  and  the  sun?  On  this  day  Jupiter 
is  said  to  be  in  opposition— -i.  e.,  the  planet  and  the  sun 
are  on  opposite  sides  of  the  earth,  and  Jupiter  then  comes 
to  the  meridian  of  any  and  every  place  at  midnight.  When 
the  sun  is  between  the  earth  and  Jupiter  (at  what  date  in 
1906?)  the  planet  is  said  to  be  in  conjunction  with  the 
sun,  and  of  course  passes  the  meridian  with  the  sun  at 
noon.  Can  you  determine  from  the  figure  the  time  at 
which  Jupiter  comes  to  the  meridian  at  other  dates  than 
opposition  and  conjunction?  Can  you  determine  when  it 
is  visible  in  the  evening  hours  ?  Tell  from  the  figure  what 
constellation  is  on  the  meridian  at  midnight  on  January 
1st.  Will  it  be  the  same  constellation  in  every  year  ? 

30.  Mercury,  Venus,  and  Mars.— Fig.  17,  which  repre- 
sents the  orbits  of  the  inner  planets,  differs  from  Fig.  16 
only  in  the  method  of  fixing  the  positions  of  the  planets 
in  their  orbits  at  any  given  date.  The  motion  of  these  plan- 
ets is  so  rapid,  on  account  of  their  proximity  to  the  sun,  that 
it  would  not  do  to  mark  their  positions  as  was  done  for 
Jupiter  and  Saturn,  and  with  the  exception  of  the  earth  they 
do  not  always  return  to  the  same  place  on  the  same  day  in 
each  year.  It  is  therefore  necessary  to  adopt  a  slightly  dif- 
ferent method,  as  follows  :  The  straight  line  extending  from 
the  sun  toward  the  vernal  equinox,  F,  is  called  the  prime 
radius,  and  we  know  from  past  observations  that  the  earth 
in  its  motion  around  the  sun  crosses  this  line  on  September 
23d  in  each  year,  and  to  fix  the  earth's  position  for  Septem- 
ber 23d  in  the  diagram  we  have  only  to  take  the  point  at 
which  the  prime  radius  intersects  the  earth's  orbit.  A 
month  later,  on  October  23d,  the  earth  will  no  longer  be  at 
this  point,  but  will  have  moved  on  along  its  orbit  to  the 


FIXED   AND   WANDERING   STARS 


point  marked  30  (thirty  days  after  September  23d).  Sixty 
days  after  September  23d  it  will  be  at  the  point  marked  60, 
etc.,  and  for  any  date  we  have  only  to  find  the  number  of 
days  intervening  between  it  and  the  preceding  September 
23d,  and  this  number  will  show  at  once  the  position  of  the 
earth  in  its  orbit.  Thus  for  the  date  July  4,  1900,  we  find 

1900,  July  4  —  1899,  September  23  =  284  days, 
and  the  little  circle  marked  upon  the  earth's  orbit  between 
the  numbers  270  and  300  shows  the  position  of  the  earth  on 
that  date. 

In  what  constellation  was  the  sun  on  July  4,  1900? 
What  zodiacal  constellation  came  to  the  meridian  at  mid- 
night on  that  date?  What  other  constellations  came  to 
the  meridian  at  the  same  time  ? 

The  positions  of  the  other  planets  in  their  orbits  are 
found  in  the  same  manner,  save  that  they  do  not  cross  the 
prime  radius-  on  the  same  date  in  each  year,  and  the  times 
at  which  they  do  cross  it  must  be  taken  from  the  following 
table : 

TABLE  OF  EPOCHS 


A.  D. 

Mercury. 

Venus. 

Earth. 

Mars. 

Period  .  .  . 
1900  
1901 

88.0  days. 
Feb.  18th. 
Feb  5th 

224.  7  days. 
Jan.  llth. 
\pril  5th 

365.25  days. 
Sept.  23d. 
Sept  23d 

687.1  days. 
April  28th. 

1902  
1903 

Jan.  23d. 
April  8th 

June  29th. 
Feb.  8th. 

Sept,  23d. 
Sept   23d 

March  16th. 

1904. 

March  25th 

May  3d. 

Sept.  23d. 

Feb.  1st. 

1905  
1906 

March  12th. 
Feb  27th 

July  26th. 
March  8th 

Sept.  23d. 
Sept   23d 

Dec.  19th. 

1907 

Feb  14th 

May  31st. 

Sept   23d 

Nov.  6th. 

1908 

Feb.  1st 

Jan.  llth. 

Sept.  23d. 

1909  
1910 

Jan.  18th. 
Jan  5th 

April  4th. 
June  28th. 

Sept.  23d. 
Sept   23d 

Sept,  23d. 

The  first  line  of  figures  in  this  table  shows  the  num- 
ber of  days  that  each  of  these  planets  requires  to  make 
a  complete  revolution  about  the  sun,  and  it  appears  from 
these  numbers  that  Mercury  makes  about  four  revolutions 


44  ASTRONOMY 

in  its  orbit  per  year,  and  therefore  crosses  the  prime  radius 
four  times  in  each  year,  while  the  other  planets  are  decid- 
edly slower  in  their  movements.  The  following  lines  of 
the  table  show  for  each  year  the  date  at  which  each  planet 
first  crossed  the  prime  radius  in  that  year;  the  dates  of 
subsequent  crossings  in  any  year  can  be  found  by  adding 
once,  twice,  or  three  times  the  period  to  the  given  date, 
and  the  table  may  be  extended  to  later  years,  if  need  be,  by 
continuously  adding  multiples  of  the  period.  In  the  case 
of  Mars  it  appears  that  there  is  only  about  one  year  out  of 
two  in  which  this  planet  crosses  the  prime  radius. 

After  the  date  at  which  the  planet  crosses  the  prime 
radius  has  been  determined  its  position  for  any  required 
date  is  found  exactly  as  in  the  case  of  the  earth,  and  the 
constellation  in  which  the  planet  will  appear  from  the 
earth  is  found  as  explained  above  in  connection  with  Jupi- 
ter and  Saturn. 

The  broken  lines  in  the  figure  represent  the  construc- 
tion for  finding  the  places  in  the  sky  occupied  by  Mercury, 
Venus,  and  Mars  on  July  4,  1900.  Let  the  student  make  a 
similar  construction  and  find  the  positions  of  these  planets 
at  the  present  time.  Look  them  up  in  the  sky  and  see  if 
they  are  where  your  work  puts  them. 

31.  Exercises. — The  "evening  star"  is  a  term  loosely 
applied  to  any  planet  which  is  visible  in  the  western  sky 
soon  after  sunset.  It  is  easy  to  see  that  such  a  planet  must 
be  farther  toward  the  east  in  the  sky  than  is  the  sun,  and 
in  either  Fig.  16  or  Fig.  17  any  planet  which  viewed  from 
the  position  of  the  earth  lies  to  the  left  of  the  sun  and 
not  more  than  50°  away  from  it  will  be  an  evening  star. 
If  to  the  right  of  the  sun  it  is  a  morning  star,  and  may  be 
seen  in  the  eastern  sky  shortly  before  sunrise. 

What  planet  is  the  evening  star  now  9  Is  there  more 
than  one  evening  star  at  a  time?  What  is  the  morning 
star  now  ? 

Do  Mercury,  Venus,  or  Mars  ever  appear  in  opposition  ? 


FIXED  AND  WANDERING  STARS  45 

What  is  the  maximum  angular  distance  from  the  sun  at 
which  \7enus  can  ever  be  seen  ?  Why  is  Mercury  a  more 
difficult  planet  to  see  than  Venus?  In  what  month  of  the 
year  does  Mars  come  nearest  to  the  earth?  Will  it  always 
be  brighter  in  this  month  than  in  any  other  ?  Which  of 
all  the  planets  comes  nearest  to  the  earth  ? 

The  earth  always  comes  to  the  same  longitude  on  the 
same  day  of  each  year.  Why  is  not  this  true  of  the  other 
planets  ? 

The  student  should  remember  that  in  one  respect  Figs. 
16  and  17  are  not  altogether  correct  representations,  since 
they  show  the  orbits  as  all  lying  in  the  same  plane.  If  this 
were  strictly  true,  every  planet  would  move,  like  the  sun, 
always  along  the  ecliptic ;  but  in  fact  all  of  the  orbits  are 
tilted  a  little  out  of  the  plane  of  the  ecliptic  and  every 
planet  in  its  motion  deviates  a  little  from  the  ecliptic,  first 
to  one  side  then  to  the  other ;  but  not  even  Mars,  which  is 
the  most  erratic  in  this  respect,  ever  gets  more  than  eight 
degrees  away  from  the  ecliptic,  and  for  the  most  part  all 
of  them  are  much  closer  to  the  ecliptic  than  this  limit. 


A  .  >->^ 


V 

CHAPTEE   IV 

CELESTIAL   MECHANICS 

32.  The  beginnings  of  celestial  mechanics.— From  the  ear- 
liest dawn  of  civilization,  long  before  the  beginnings  of 
written  history,  the  motions  of  sun  and  moon  and  planets 
among  the  stars  from  constellation  to  constellation  had 
commanded  the  attention  of  thinking  men,  particularly  of 
the  class  of  priests.  The  religions  of  which  they  were  the 
guardians  and  teachers  stood  in  closest  relations  with  the 
movements  of  the  stars,  and  their  own  power  and  influence 
were  increased  by  a  knowledge  of  them. 

Out  of  these  professional  needs,  as  well  as  from  a  spirit 
of  scientific  research,  there  grew  up  and  flourished  for 
many  centuries  a  study  of  the  motions  of  the  planets,  sim- 
ple and  crude  at  first,  because  the  observations  that  could 
then  be  made  were  at  best  but  rough  ones,  but  growing 
more  accurate  and  more  complex  as  the  development  of  the 
mechanic  arts  put  better  and  more  precise  instruments  into 
the  hands  of  astronomers  and  enabled  them  to  observe  with 
increasing  accuracy  the  movements  of  these  bodies.  It  was 
early  seen  that  while  for  the  most  part  the  planets,  includ- 
ing the  sun  and  moon,  traveled  through  the  constellations 
from  west  to  east,  some  of  them  sometimes  reversed  their 
motion  and  for  a  time  traveled  in  the  opposite  way.  This 
clearly  can  not  be  explained  by  the  simple  theory  which 
had  early  been  adopted  that  a  planet  moves  always  in  the 
same  direction  around  a  circular  orbit  having  the  earth  at 
its  center,  and  so  it  was  said  to  move  around  in  a  small 
circular  orbit,  called  an  epicycle,  whose  center  was  situated 
46 


ISAAC  NEWTON   ( 1643-1727 ). 


CELESTIAL  MECHANICS  47 

upon  and  moved  along  a  circular  orbit,  called  the  deferent, 
within  which  the  earth  was  placed,  as  is  shown  in  Fig.  18, 
where  the  small  circle  is  the  epicycle,  the  large  circle  is  the 
deferent,  P  is  the  planet,  and  E  the  earth.  When  this 
proved  inadequate  to  account  for  the  really  complicated 
movements  of  the  planets,  another  epicycle  was  put  on  top 
of  the  first  one,  and  then  another  and  another,  until  the 
supposed  system  became  so  complicated  that  Copernicus,  a 
Polish  astronomer,  repudiated 
its  fundamental  theorem  and 
taught  that  the  motions  of 
the  planets  take  place  in  cir- 
cles around  the  sun  instead 
of  about  the  earth,  and  that 
the  earth  itself  is  only  one  of 
the  planets  moving  around 
the  sun  in  its-  own  appropri- 
ate orbit  and  itself  largely  re- 
sponsible for  the  seemingly 

&  J  FIG.  18.— Epicycle  and  deferent. 

erratic     movements    of     the 

other  planets,  since  from  day  to  day  we  see  them  and  ob- 
serve their  positions  from  different  points  of  view. 

33.  Kepler's  laws. — Two  generations  later  came  Kepler 
with  his  three  famous  laws  of  planetary  motion : 

I.  Every  planet  moves  in  an  ellipse  which  has  the  sun 
at  one  of  its  foci. 

II.  The  radius  vector  of  each  planet  moves  over  equal 
areas  in  equal  times. 

III.  The  squares  of  the  periodic  times  of  the  planets 
are  proportional  to  the  cubes  of  their  mean  distances  from 
the  sun. 

These  laws  are  the  crowning  glory,  not  only  of  Kepler's 
career,  but  of  all  astronomical  discovery  from  the  begin- 
ning up  to  his  time,  and  they  well  deserve  careful  study 
and  explanation,  although  more  modern  progress  has  shown 
that  they  are  only  approximately  true. 


48  ASTRONOMY 

EXERCISE  17. — Drive  two  pins  into  a  smooth  board  an 
inch  apart  and  fasten  to  them  the  ends  of  a  string  a  foot 
long.  Take  up  the  slack  of  the  string  with  the  point  of  a 
lead  pencil  and,  keeping  the  string  drawn  taut,  move  the 
pencil  point  over  the  board  into  every  possible  position. 
The  curve  thus  traced  will  be  an  ellipse  having  the  pins  at 
the  two  points  which  are  called  its  foci. 

In  the  case  of  the  planetary  orbits  one  focus  of  the 
ellipse  is  vacant,  and,  in  accordance  with  the  first  law,  the 
center  of  the  sun  is  at  the  other  focus.  In  Fig.  17  the  dot, 
inside  the  orbit  of  Mercury,  which  is  marked  «,  shows  the 
position  of  the  vacant  focus  of  the  orbit  of  Mars,  and  the 
dot  b  is  the  vacant  focus  of  Mercury's  orbit.  The  orbits  of 
Venus  and  the  earth  are  so  nearly  circular  that  their  vacant 
foci  lie  very  close  to  the  sun  and  are  not  marked  in  the 
figure.  The  line  drawn  from  the  sun  to  any  point  of  the 
orbit  (the  string  from  pin  to  pencil  point)  is  a  radius  vector. 
The  point  midway  between  the  pins  is  the  center  of  the 
ellipse,  and  the  distance  of  either  pin  from  the  center  meas- 
ures the  eccentricity  of  the  ellipse. 

Draw  several  ellipses  with  the  same  length  of  string, 
but  with  the  pins  at  different  distances  apart,  and  note  that 
the  greater  the  eccentricity  the  flatter  is  the  ellipse,  but 
that  all  of  them  have  the  same  length.- 

If  both  pins  were  driven  into  the  same  hole,  what  kind 
of  an  ellipse  would  you  get  ? 

The  Second  Law  was  worked  out  by  Kepler  as  his  answer 
to  a  problem  suggested  by  the  first  law.  In  Fig.  17  it  is 
apparent  from  a  mere  inspection  of  the  orbit  of  Mercury 
that  this  planet  travels  much  faster  on  one  side  of  its  orbit 
than  on  the  other,  the  distance  covered  in  ten  days  between 
the  numbers  10  and  20  being  more  than  fifty  per  cent  greater 
than  that  between  50  and  60.  The  same  difference  is  found, 
though  usually  in  less  degree,  for  every  other  planet,  and 
Kepler's  problem  was  to  discover  a  means  by  which  to 
mark  upon  the  orbit  the  figures  showing  the  positions  of 


CELESTIAL  MECHANICS  49 

the  planet  at  the  end  of  equal  intervals  of  time.  His  solu- 
tion of  this  problem,  contained  in  the  second  law,  asserts 
that  if  we  draw  radii  vectores  from  the  sun  to  each  of  the 
marked  points  taken  at  equal  time  intervals  around  the 
orbit,  then  the  area  of  the  sector  formed  by  two  adjacent 
radii  vectores  and  the  arc  included  between  them  is  equal 
to  the  area  of  each  and  every  other  such  sector,  the  short 
radii  vectores  being  spread  apart  so  as  to  include  a  long 
arc  between  them  while  the  long  radii  vectores  have  a  short 
arc.  In  Kepler's  form  of  stating  the  law  the  radius  vector 
is  supposed  to  travel  with  the  planet  and  in  each  day  to 
sweep  over  the  same  fractional  part  of  the  total  area  of  the 
orbit.  The  spacing  of  the  numbers  in  Fig.  17  was  done  by 
means  of  this  law. 

For  the  proper  understanding  of  Kepler's  Third  Law  we 
must  note  that  the  "  mean  distance  "  which  appears  in  it  is 
one  half  of  the  long  diameter  of  the  orbit  and  that  the 
"periodic  time"  means  the  number  of  days  or  years  re- 
quired by  the  planet  to  make  a  complete  circuit  in  its  orbit. 
Representing  the  first  of  these  by  a  and  the  second  by  T, 
we  have,  as  the  mathematical  equivalent  of  the  law, 


where  the  quotient,  (7,  is  a  number  which,  as  Kepler  found, 
is  the  same  for  every  planet  of  the  solar  system.  If  we  take 
the  mean  distance  of  the  earth  from  the  sun  as  the  unit  of 
distance,  and  the  year  as  the  unit  of  time,  we  shall  find  by 
applying  the  equation  to  the  earth's  motion,  C  =  1.  Ap- 
plying this  value  to  any  other  planet  we  shall  find  in  the 
same  units,  a  =  T  ,  by  means  of  which  we  may  determine 
the  distance  of  any  planet  from  the  sun  when  its  periodic 
time,  I7,  has  been  learned  from  observation. 

EXERCISE  18.  —  Uranus  requires  84  years  to  make  a 
revolution  in  its  orbit.  What  is  its  mean  distance  from  the 
sun  ?  What  are  the  mean  distances  of  Mercury,  Venus,  and 
Mars  ?  (See  Chapter  III  for  their  periodic  times.)  Would 


50  ASTRONOMY 

it  be  possible  for  two  planets  at  different  distances  from 
the  sun  to  move  around  their  orbits  in  the  same  time  ? 

A  circle  is  an  ellipse  in  which  the  two  foci  have  been 
brought  together.  Would  Kepler's  laws  hold  true  for  such 
an  orbit  ? 

34.  Newton's  laws  of  motion, — Kepler  studied  and  de- 
scribed the  motion  of  the  planets.  Newton,  three  genera- 
tions later  (1727  A.  D.),  studied  and  described  the  mechan- 
ism which  controls  that  motion.  To  Kepler  and  his  age  the 
heavens  were  supernatural,  while  to  Newton  and  his  suc- 
cessors they  are  a  part  of  Nature,  governed  by  the  same 
laws  which  obtain  upon  the  earth,  and  we  turn  to  the  ordi- 
nary things  of  everyday  life  as  the  foundation  of  celestial 
mechanics. 

Every  one  who  has  ridden  a  bicycle  knows  that  he  can 
coast  farther  upon  a  level  road  if  it  is  smooth  than  if  it  is 
rough ;  but  however  smooth  and  hard  the  road  may  be  and 
however  fast  the  wheel  may  have  been  started,  it  is  sooner 
or  later  stopped  by  the  resistance  which  the  road  and  the 
air  offer  to  its  motion,  and  when  once  stopped  or  checked 
it  can  be  started  again  only  by  applying  fresh  power.  We 
have  here  a  familiar  illustration  of  what  is  called 

The  first  law  of  motion.—"  Every  body  continues  in  its 
state  of  rest  or  of  uniform  motion  in  a  straight  line  except 
in  so  far  as  it  may  be  compelled  by  force  to  change  that 
state."  A  gust  of  wind,  a  stone,  a  careless  movement  of 
the  rider  may  turn  the  bicycle  to  the  right  or  the  left,  but 
unless  some  disturbing  force  is  applied  it  will  go  straight 
ahead,  and  if  all  resistance  to  its  motion  could  be  removed 
it  would  go  always  at  the  speed  given  it  by  the  last  power 
applied,  swerving  neither  to  the  one  hand  nor  the  other. 

When  a  slow  rider  increases  his  speed  we  recognize  at 
once  that  he  has  applied  additional  power  to  the  wheel,  and 
when  this  speed  is  slackened  it  equally  shows  that  force  has 
been  applied  against  the  motion.  It  is  force  alone  which 
can  produce  a  change  in  either  velocity  or  direction  of 


CELESTIAL  MECHANICS  51 

motion ;  but  simple  as  this  law  now  appears  it  required  the 
genius  of  Galileo  to  discover  it  and  of  Newton  to  give  it  the 
form  in  which  it  is  stated  above. 

35.  The  second  law  of  motion,  which  is  also  due  to  Gali- 
leo and  Newton,  is : 

"  Change  of  motion  is  proportional  to  force  applied  and 
takes  place  in  the  direction  of  the  straight  line  in  which 
the  force  acts."  Suppose  a  man  to  fall  from  a  balloon  at 
some  great  elevation  in  the  air ;  his  own  weight  is  the  force 
which  pulls  him  down,  and  that  force  operating  at  every 
instant  is  sufficient  to  give  him  at  the  end  of  the  first  sec- 
ond of  his  fall  a  downward  velocity  of  32  feet  per  second — 
i.  e.,  it  has  changed  his  state  from  rest,  to  motion  at  this 
rate,  and  the  motion  is  toward  the  earth  because  the  force 
acts  in  that  direction.  During  the  next  second  the  cease- 
less operation  of  this  force  will  have  the  same  effect  as  in 
the  first  second  and  will  add  another  32  feet  to  his  ve- 
locity, so  that  two  seconds  from  the  time  he  commenced  to 
fall  he  will  be  moving  at  the  rate  of  64  feet  per  second,  etc. 
The  column  of  figures  marked  v  in  the  table  below  shows 
what  his  velocity  will  be  at  the  end  of  subsequent  seconds. 
The  changing  velocity  here  shown  is  the  change  of  motion 
to  which  the  law  refers,  and  the  velocity  is  proportional  to 
the  time  shown  in  the  first  column  of  the  table,  because  the 
amount  of  force  exerted  in  this  case  is  proportional  to  the 
time  during  which  it  operated.  The  distance  through 
which  the  man  will  fall  in  each  second  is  shown  in  the  col- 
umn marked  d,  and  is  found  by  taking  the  average  of  his 
velocity  at  the  beginning  and  end  of  this  second,  and  the 
total  distance  through  which  he  has  fallen  at  the  end  of 
each  second,  marked  s  in  the  table,  is  found  by  taking  the 
sum  of  all  the  preceding  values  of  d.  The  velocity,  32  feet 
per  second,  which  measures  the  change  of  motion  in  each 
second,  also  measures  the  accelerating  force  which  produces 
this  motion,  and  it  is  usually  represented  in  formulae  by 
the  letter  g.  Let  the  student  show  from  the  numbers  in 


52  ASTRONOMY 

the  table  that  the  accelerating  force,  the  time,  ^,  during 
which  it  operates,  and  the  space,  s,  fallen  through,  satisfy 
the  relation 

s  =  |  g  t2, 

which  is  usually  called  the  law  of  falling  bodies.  How  does 
the  table  show  that  g  is  equal  to  32  ? 


TABLE 

t 

V 

d 

s 

0 

0 

0 

0 

1 

32 

16 

16 

2 

64 

48 

64 

3 

96 

80 

144 

4 

128 

112 

256 

5 

160 

144 

400 

etc.      etc.        etc.        etc. 

If  the  balloon  were  half  a  mile  high  how  long  would  it 
take  to  fall  to  the  ground  ?  What  would  be  the  velocity 
just  before  reaching  the  ground  ? 

Fig.  19  shows  the  path  through  the  air  of  a  ball  which 
has  been  struck  by  a  bat  at  the  point  A,  and  started  off  in 
the  direction  A  B  with  a  velocity  of  200  feet  per  second. 
In  accordance  with  the  first  law  of  motion,  if  it  were  acted 
upon  by  no  other  force  than  the  impulse  given  by  the  bat, 
it  should  travel  along  the  straight  line  A  S  at  the  uniform 
rate  of  200  feet  per  second,  and  at  the  end  of  the  fourth 
second  it  should  be  800  feet  from  A,  at  the  point  marked  4, 
but  during  these  four  seconds  its  weight  has  caused  it  to 
fall  256  feet,  and  its  actual  position,  4',  is  256  feet  below 
the  point  4.  In  this  way  we  find  its  position  at  the  end  of 
each  second,  1',  2',  3',  4',  etc.,  and  drawing  a  line  through 
these  points  we  shall  find  the  actual  path  of  the  ball  under 
the  influence  of  the  two  forces  to  be  the  curved  line  A  C. 
No  matter  how  far  the  ball  may  go  before  striking  the 
ground,  it  can  not  get  back  to  the  point  A,  and  the  curve 


GALILEO  GALILEI   (1564-1642). 


CELESTIAL   MECHANICS 


53 


A  C  therefore  can  not  be  a  part  of  a  circle,  since  that  curve 
returns  into  itself.  It  is,  in  fact,  a  part  of  a  parabola, 
which,  as  we  shall  see  later,  is  a  kind  of  orbit  in  which 
comets  and  some  other  heavenly  bodies  move.  A  skyrocket 


FIG.  19.— The  path  of  a  ball. 

moves  in  the  same  kind  of  a  path,  and  so  does  a  stone,  a 
bullet,  or  any  other  object  hurled  through  the  air. 

36.  The  third  law  of  motion. — "  To  every  action  there  is 
always  an  equal  and  contrary  reaction  ;  or  the  mutual  ac- 
tions of  any  two  bodies  are  always  equal  and  oppositely 
directed."  This  is  well  illustrated  in  the  case  of  a  man 
climbing  a  rope  hand  over  hand.  The  direct  force  or  action 
which  he  exerts  is  a  downward  pull  upon  the  rope,  and  it  is 
the  reaction  of  the  rope  to  this  pull  which  lifts  him  along 
it.  We  shall  find  in  a  later  chapter  a  curious  application 
of  this  law  to  the  history  of  the  earth  and  moon. 


54  ASTRONOMY 

It  is  the  great  glory  of  Sir  Isaac  Newton  that  he  first  of 
all  men  recognized  that  these  simple  laws  of  motion  hold 
true  in  the  heavens  as  well  as  upon  the  earth ;  that  the 
complicated  motion  of  a  planet,  a  comet,  or  a  star  is  de- 
termined in  accordance  with  these  laws  by  the  forces 
which  act  upon  the  bodies,  and  that  these  forces  are 
essentially  the  same  as  that  which  we  call  weight.  The 
formal  statement  of  the  principle  last  named  is  in- 
cluded in — 

37.  Newton's  law  of  gravitation, — "  Every  particle  of 
matter  in  the  universe  attracts  every  other  particle  with  a 
force  whose  direction  is  that  of  a  line  joining  the  two,  and 
whose  magnitude  is  directly  as  the  product  of  their  masses, 
and  inversely  as  the  square  of  their  distance  from  each 
other."  We  know  that  we  ourselves  and  the  things  about 
us  are  pulled  toward  the  earth  by  a  force  (weight)  which  is 
called,  in  the  Latin  that  Newton  wrote,  gravitas,  and  the 
word  marks  well  the  true  significance  of  the  law  of  gravita- 
tion. Newton  did  not  discover  a  new  force  in  the  heavens, 
but  he  extended  an  old  and  familiar  one  from  a  limited 
terrestrial  sphere  of  action  to  an  unlimited  and  celestial 
one,  and  furnished  a  precise  statement  of  the  way  in  which 
the  force  operates.  Whether  a  body  be  hot  or  cold,  wet  or 
dry,  solid,  liquid,  or  gaseous,  is  of  no  account  in  deter- 
mining the  force  which  it  exerts,  since  this  depends  solely 
upon  mass  and  distance. 

The  student  should  perhaps  be  warned  against  straining 
too  far  the  language  which  it  is  customary  to  employ  in 
this  connection.  The  law  of  gravitation  is  certainly  a  far- 
reaching  one,  and  it  may  operate  in  every  remotest  corner 
of  the  universe  precisely  as  stated  above,  but  additional 
information  about  those  corners  would  be  welcome  to  sup- 
plement our  rather  scanty  stock  of  knowledge  concerning 
what  happens  there.  We  may  not  controvert  the  words  of_J>- 
a  popular  preacher  who  says,  "  When  I  lift  my  hand  I  move 
the  stars  in  Ursa  Major,"  but  we  should  not  wish  to  stand 


CELESTIAL  MECHANICS  55 

sponsor  for  them,  even  though  they  are  justified  by  a  rigor- 
ous interpretation  of  the  Newtonian  law. 

The  word  mass,  in  the  statement  of  the  law  of  gravita- 
tion, means  the  quantity  of  matter  contained  in  the  body, 
and  if  we  represent  by  the  letters  m'  and  m"  the  respective 
quantities  of  matter  contained  in  the  two  bodies  whose  dis- 
tance from  each  other  is  r,  we  shall  have,  in  accordance 
with  the  law  of  gravitation,  the  following  mathematical 
expression  for  the  force,  F,  which  acts  between  them  : 


This  equation,  which  is  the  general  mathematical  ex- 
pression for  the  law  of  gravitation,  may  be  made  to  yield 
some  curious  results.  Thus,  if  we  select  two  bullets,  each 
having  a  mass  of  1  gram,  and  place  them  so  that  their  qen- 
ters  are  1  centimeter  apart,  the  above  expression  for  the 
force  exerted  between  them  becomes 


from  which  it  appears  that  the  coefficient  Ic  is  the  force 
exerted  between  these  bodies.  This  is  called  the  gravita- 
tion constant,  and  it  evidently  furnishes  a  measure  of  the 
specific  intensity  with  which  one  particle  of  matter  attracts 
another.  Elaborate  experiments  which  have  been  made  to 
determine  the  amount  of  this  force  show  that  it  is  sur- 
prisingly small,  for  in  the  case  of  the  two  bullets  whose 
mass  of  1  gram  each  is  supposed  to  be  concentrated  into 
an  indefinitely  small  space,  gravity  would  have  to  operate 
between  them  continuously  for  more  than  forty  minutes  in 
order  to  pull  them  together,  although  they  were  separated 
by  only  1  centimeter  to  start  with,  and  nothing  save  their 
own  inertia  opposed  their  movements.  It  is  only  when  one 
or  both  of  the  masses  m\  m"  are  very  great  that  the  force 
of  gravity  becomes  large,  and  the  weight  of  bodies  at  the 


56  ASTRONOMY 

surface  of  the  earth  is  considerable  because  of  the  great 
quantity  of  matter  which  goes  to  make  up  the  earth. 
Many  of  th'e  heavenly  bodies  are  much  more  massive  than 
the  earth,  as  the  mathematical  astronomers  have  found  by 
applying  the  law  of  gravitation  to  determine  numerically 
their  masses,  or,  in  more  popular  language,  to  "  weigh " 
them. 

The  student  should  observe  that  the  two  terms  mass 
and  weight  are  not  synonymous ;  mass  is  defined  above  as 
the  quantity  of  matter  contained  in  a  body,  while  weight 
is  the  force  with  which  the  earth  attracts  that  body,  and 
in  accordance  with  the  law  of  gravitation  its  weight  de- 
pends upon  its  distance  from  the  center  of  the  earth,  while 
its  mass  is  quite  independent  of  its  position  with  respect 
to  the  earth. 

By  the  third  law  of  motion  the  earth  is  pulled  toward  a 
falling  body  just  as  strongly  as  the  body  is  pulled  toward 
the  earth — i.  e.,  by  a  force  equal  to  the  weight  of  the  body. 
How  much  does  the  earth  rise  toward  the  body  ? 

38.  The  motion  of  a  planet. — In  Fig.  20  /S  represents  the 
sun  and  P  a  planet  or  other  celestial  body,  which  for  the 
moment  is  moving  along  the  straight  line  P  1.  In  accord- 
ance with  the  first  law  of  motion  it  would  continue  to  move 
along  this  line  with  uniform  velocity  if  no  external  force 
acted  upon  it;  but  such  a  force,  the  sun's  attraction,  is 
acting,  and  by  virtue  of  this  attraction  the  body  is  pulled 
aside  from  the  line  P  1. 

Knowing  the  velocity  and  direction  of  the  body's  motion 
and  the  force  with  which  the  sun  attracts  it,  the  mathema- 
tician is  able  to  apply  Newton's  laws  of  motion  so  as  to 
determine  the  path  of  the  body,  and  a  few  of  the  possible 
orbits  are  shown  in  the  figure  where  the  short  cross  stroke 
marks  the  point  of  each  orbit  which  is  nearest  to  the  sun. 
This  point  is  called  the  perihelion. 

Without  any  formal  application  of  mathematics  we  may 
readily  see  that  the  swifter  the  motion  of  the  body  at  P 


CELESTIAL   MECHANICS 


the  shorter  will  he  the  time  during  which  it  is  subjected  to 
the  sun's  attraction  at  close  range,  and  therefore  the  force 
exerted  by  the  sun,  and  the  resulting  change  of  motion,  will 
be  small,  as  in  the  orbits  P  1  and  P  2. 

On  the  other  hand,  P  5  and  P  6  represent  orbits  in  which 
the  velocity  at  P  was  comparatively  small,  and  the  resulting 
change   of    motion   greater 
than  would  be  possible  for 
a  more  swiftly  moving  body. 

What  would  be  the  or_ 
bit  if  the  velocity  at  P  were 
reduced  to  nothing  at  all  ? 

What  would  be  the  effect 
if  the  body  starting  at  P 
moved  directly  away  from  1? 

The  student  should  not 
fail  to  observe  that  the  sun's 
attraction  tends  to  pull  the 
body  at  P  forward  along  its 
path,  and  therefore  increas- 
es its  velocity,  and  that  this 
influence  continues  until 

the  planet  reaches  perihelion,  at  which  point  it  attains  its 
greatest  velocity,  and  the  force  of  the  sun's  attraction  is 
wholly  expended  in  changing  the  direction  of  its  motion. 
After  the  planet  has  passed  perihelion  the  sun  begins  to 
pull  backward  and  to  retard  the  motion  in  just  the  same 
measure  that  before  perihelion  passage  it  increased  it,  so 
that  the  two  halves  of  the  orbit  on  opposite  sides  of  a  line 
drawn  from  the  perihelion  through  the  sun  are  exactly 
alike.  We  may  here  note  the  explanation  of  Kepler's  sec- 
ond law :  when  the  planet  is  near  the  sun  it  moves  faster, 
and  the  radius  vector  changes  its  direction  more  rapidly 
than  when  the  planet  is  remote  from  the  sun  on  account 
of  the  greater  force  with  which  it  is  attracted,  and  the  ex- 
act relation  between  the  rates  at  which  the  radius  vector 


FIG.  20.— Different  kinds  of  orbits. 


58  ASTRONOMY 

turns  in  different  parts  of  the  orbit,  as  given  by  the  second 
law,  depends  upon  the  changes  in  this  force. 

When  the  velocity  is  not  too  great,  the  sun's  backward 
pull,  after  a  planet  has  passed  perihelion,  finally  overcomes 
it  and  turns  the  planet  toward  the  sun  again,  in  such  a  way 
that  it  comes  back  to  the  point  P,  moving  in  the  same  di- 
rection and  with  the  same  speed  as  before — i.  e.,  it  has  gone 
around  the  sun  in  an  orbit  like  P  6  or  P  4,  an  ellipse,  along 
which  it  will  continue  to  move  ever  after.  But  we  must 
not  fail  to  note  that  this  return  into  the  same  orbit  is  a 
consequence  of  the  last  line  in  the  statement  of  the  law  of 
gravitation  (p.  54),  and  that,  if  the  magnitude  of  this  force 
were  inversely  as  the  cube  of  the  distance  or  any  other  pro- 
portion than  the  square,  the  orbit  would  be  something  very 
different.  If  the  velocity  is  too  great  for  the  sun's  attrac- 
tion to  overcome,  the  orbit  will  be  a  hyperbola,  like  P  2, 
along  which  the  body  will  move  away  never  to  return,  while 
a  velocity  just  at  the  limit  of  what  the  sun  can  control  gives 
an  orbit  like  P  3,  a  parabola,  along  which  the  body  moves 
with  parabolic  velocity,  which  is  ever  diminishing  as  the 
body  gets  farther  from  the  sun,  but  is  always  just  sufficient 
to  keep  it  from  returning.  If  the  earth's  velocity  could  be 
increased  41  per  cent,  from  19  up  to  27  miles  per  second,  it 
would  have  parabolic  velocity,  and  would  quit  the  sun's 
company. 

The  summation  of  the  whole  matter  is  that  the  orbit  in 
which  a  body  moves  around  the  sun,  or  past  the  sun,  de- 
pends upon  its  velocity  and  if  this  velocity  and  the  direc- 
tion of  the  motion  at  any  one  point  in  the  orbit  are  known 
the  whole  orbit  is  determined  by  them,  and  the  position  of 
the  planet  in  its  orbit  for  past  as  well  as  future  times  can 
be  determined  through  the  application  of  Newton's  laws ; 
and  the  same  is  true  for  any  other  heavenly  body — moon, 
comet,  meteor,  etc.  It  is  in  this  way  that  astronomers  are 
able  to  predict,  years  in  advance,  in  what  particular  part  of 
the  sky  a  given  planet  will  appear  at  a  given  time. 


CELESTIAL  MECHANICS  59 

It  is  sometimes  a  source  of  wonder  that  the  planets 
move  in  ellipses  instead  of  circles,  but  it  is  easily  seen  from 
Fig.  20  that  the  planet,  P,  could  not  by  any  possibility 
move  in  a  circle,  since  the  direction  of  its  motion  at  P  is 
not  at  right  angles  with  the  line  joining  it  to  the  sun  as  it 
must  be  in  a  circular  orbit,  and  even  if  it  were  perpen- 
dicular to  the  radius  vector  the  planet  must  needs  have 
exactly  the  right  velocity  given  to  it  at  this  point,  since 
either  more  or  less  speed  would  change  the  circle  into  an 
ellipse.  In  order  to  produce  circular  motion  there  must  be 
a  balancing  of  conditions  as  nice  as  is  required  to  make  a 
pin  stand  upon  its  point,  and  the  really  surprising  thing  is 
that  the  orbits  of  the  planets  should  be  so  nearly  circular 
as  they  are.  If  the  orbit  of  the  earth  were  drawn  accu- 
rately to  scale,  the  untrained  eye  would  not  detect  the 
slightest  deviation  from  a  true  circle,  and  even  the  orbit  of 
Mercury  (Fig.  17),  which  is  much  more 
eccentric  than  that  of  the  earth,  might  al- 
most pass  for  a  circle. 

The  orbit  P  2,  which  lies  between  the 
parabola  and  the  straight  line,  is  called  in 
geometry  a  hyperbola,   and   Newton   suc- 
ceeded in  proving  from  the  law  of  gravita- 
tion that  a  body  might  move  under  the 
sun's  attraction  in  a  hyperbola  as  well  as 
in  a  parabola  or  ellipse  ;  but  it  must  move 
in  some  one  of  these  curves ;  no  other  or- 
bit is  possible.*      Thus  it  would  not  be    An  orbit. 
possible  for  a  body  moving  under  the  law 
of  gravitation  to  describe   about  the  sun  any  such  orbit 
as  is  shown  in  Fig.  21.     If  the  body  passes  a  second  time 
through  any  point  of  its  orbit,  such  as  P  in  the  figure,  then 
it  must  retrace,  time  after  time,  the  whole  path  that  it  first 

*  The  circle  and  straight  line  are  considered  to  be  special  cases  of 
these  curves,  which,  taken  collectively,  are  called  the  conic  sections. 


60  ASTRONOMY 

traversed  in  getting  from  P  around  to  P  again — i.  e.,  the 
orbit  must  be  an  ellipse. 

Newton  also  proved  that  Kepler's  three  laws  are  mere 
corollaries  from  the  law  of  gravitation,  and  that  to  be 
strictly  correct  the  third  law  must  be  slightly  altered  so  as 
to  take  into  account  the  masses  of  the  planets.  These  are, 
however,  so  small  in  comparison  with  that  of  the  sun,  that 
the  correction  is  of  comparatively  little  moment. 

39.  Perturbations. — In  what  precedes  we  have  considered 
the  motion  of  a  planet  under  the  influence  of  no  other 
force  than  the  sun's  attraction,  while  in  fact,  as  the  law  of 
gravitation  asserts,  every  other  body  in  the  universe  is  in 
some  measure  attracting  it  and  changing  its  motion.  The 
resulting  disturbances  in  the  motion  of  the  attracted  ,body 
are  called  perturbations,  but  for  the  most  part  these  are 
insignificant,  because  the  bodies  by  whose  disturbing  attrac- 
tions they  are  caused  are  either  very  small  or  very  remote, 
and  it  is  only  when  our  moving  planet,  P,  comes  under  the 
influence  of  some  great  disturbing  power  like  Jupiter  or 
one  of  the  other  planfets  that  the  perturbations  caused  by 
their  influence  need  to  be  taken  into  account. 

The  problem  of  the  motion  of  three  bodies — sun,  Jupiter, 
planet — which  must  then  be  dealt  with  is  vastly  more  com- 
plicated than  that  which  we  have  considered,  and  the  ablest 
mathematicians  and  astronomers  have  not  been  able  to  fur- 
nish a  complete  solution  for  it,  although  they  have  worked 
upon  the  problem  for  two  centuries,  and  have  developed  an 
immense  amount  of  detailed  information  concerning  it. 

In  general  each  planet  works  ceaselessly  upon  the  orbit 
of  every  other,  changing  its  size  and  shape  and  position, 
backward  and  forward  in  accordance  with  the  law  of  gravi- 
tation, and  it  is  a  question  of  serious  moment  how  far  this 
process  may  extend.  If  the  diameter  of  the  earth's  orbit 
were  very  much  increased  or  diminished  by  the  perturbing 
action  of  the  other  planets,  the  amount  of  heat  received 
from  the  sun  would  be  correspondingly  changed,  and  the 


CELESTIAL   MECHANICS  61 

earth,  perhaps,  be  rendered  unfit  for  the  support  of  life. 
The  tipping  of  the  plane  of  the  earth's  orbit  into  a  new 
position  might  also  produce  serious  consequences ;  but  the 
great  French  mathematician  of  a  century  ago,  Laplace, 
succeeded  in  proving  from  the  law  of  gravitation  that  al- 
though both  of  these  changes  are  actually  in  progress  they 
can  not,  at  least  for  millions  of  years,  go  far  enough  to 
prove  of  serious  consequence,  and  the  same  is  true  for  all 
the  other  planets,  unless  here  and  there  an  asteroid  may 
prove  an  exception  to  the  rule. 

The  precession  (Chapter  V)  is  a  striking  illustration 
of  a  perturbation  of  slightly  different  character  from  the 
above,  and  another  is  found  in  connection  with  the  plane 
of  the  moon's  orbit.  It  will  be  remembered  that  the  moon 
in  its  motion  among  the  stars  never  goes  far  from  the 
ecliptic,  but  in  a  complete  circuit  of  the  heavens  crosses  it 
twice,  once  -in  going  from  south  to  north  and  once  in  the 
opposite  direction.  The  points  at  which  it  crosses  the 
ecliptic  are  called  the  nodes,  and  under  the  perturbing  in- 
fluence of  the  sun  these  nodes  move  westward  along  the 
ecliptic  about  twenty  degrees  per  year,  an  extraordinarily 
rapid  perturbation,  and  one  of  great  consequence  in  the 
theory  of  eclipses. 

40.  Weighing  the  planets. — Although  these  perturbations 
can  not  be  considered  dangerous,  they  are  interesting  since 
they  furnish  a  method  for  weighing  the  planets  which  pro- 
duce them.  From  the  law  of  gravitation  we  learn  that  the 
ability  of  a  planet  to  produce  perturbations  depends  di- 
rectly upon  its  mass,  since  the  force  F  which  it  exerts  con- 
tains this  mass,  m',  as  a  factor.  So,  too,  the  divisor  r2  in 
the  expression  for  the  force  shows  that  the  distance  be- 
tween the  disturbing  and  disturbed  bodies  is  a  matter  of 
great  consequence,  for  the  smaller  the  distance  the  greater 
the  force.  When,  therefore,  the  mass  of  a  planet  such  as 
Jupiter  is  to  be  determined  from  the  perturbations  it  pro- 
duces, it  is  customary  to  select  some  such  opportunity  as 


62 


ASTRONOMY 


FIG.  22. — A  planet  subject  to  great  per- 
turbations by  Jupiter. 


is  presented  in  Fig.  22,  where  one  of  the  small  planets, 
called  asteroids,  is  represented  as  moving  in  a  very  eccen- 
tric orbit,  which  at  one  point  approaches  close  to  the  orbit 
of  Jupiter,  and  at  another  place  comes  near  to  the  orbit  of 

the  earth.  For  the  most  part 
Jupiter  will  not  exert  any 
very  great  disturbing  influ- 
ence upon  a  planet  moving  in 
such  an  orbit  as  this,  since  it 
is  only  at  rare  intervals  that 
the  asteroid  and  Jupiter  ap- 
proach so  close  to  each  other, 
as  is  shown  in  the  figure. 
The  time  during  which  the 
asteroid  is  little  aifected  by 
the  attraction  of  Jupiter  is 
used  to  study  the  motion  giv- 
en to  it  by  the  sun's  attrac- 
tion— that  is,  to  determine  carefully  the  undisturbed  orbit 
in  which  it  moves ;  but  there  comes  a  time  at  which  the 
asteroid  passes  close  to  Jupiter,  as  shown  in  the  figure,  and 
the  orbital  motion  which  the  sun  imparts  to  it  will  then  be 
greatly  disturbed,  and  when  the  planet  next  comes  round 
to  the  part  of  its  orbit  near  the  earth  the  effect  of  these 
disturbances  upon  its  apparent  position  in  the  sky  will  be 
exaggerated  by  its  close  proximity  to  the  earth.  If  now 
the  astronomer  observes  the  actual  position  of  the  asteroid 
in  the  sky,  its  right  ascension  and  declination,  and  com- 
pares these  with  the  position  assigned  to  the  planet  by  the 
law  of  gravitation  when  the  attraction  of  Jupiter  is  ignored, 
the  differences  between  the  observed  right  ascensions  and 
declinations  and  those  computed  upon  the  theory  of  undis- 
turbed motion  will  measure  the  influence  that  Jupiter  has 
had  upon  the  asteroid,  and  the  amount  by  which  Jupiter  has 
shifted  it,  compared  with  the  amount  by  which  the  sun  has 
moved  it — that  is,  with  the  motion  in  its  orbit — furnishes 


CELESTIAL  MECHANICS  63 

the  mass  of  Jupiter  expressed  as  a  fractional  part  of  the 
mass  of  the  sun. 

There  has  been  determined  in  this  manner  the  mass  of 
every  planet  in  the  solar  system  which  is  large  enough  to 
produce  any  appreciable  perturbation,  and  all  these  masses 
prove  to  be  exceedingly  small  fractions  of  the  mass  of  the 
sun,  as  may  be  seen  from  the  following  table,  in  which  is 
given  opposite  the  name  of  each  planet  the  number  by 
which  the  mass  of  the  sun  must  be  divided  in  order  to 
get  the  mass  of  the  planet : 

Mercury 7,000,000  (?) 

Venus 408,000 

Earth 329,000 

Mars 3,093,500 

Jupiter 1,047.4 

Saturn 3,502 

Uranus 22,800 

Neptune 19,700 

It  is  to  be  especially  noted  that  the  mass  given  for  each 
planet  includes  the  mass  of  all  the  satellites  which  attend 
it,  since  their  influence  was  felt  in  the  perturbations  from 
which  the  mass  was  derived.  Thus  the  mass  assigned  to 
the  earth  is  the  combined  mass  of  earth  and  moon. 

41.  Discovery  of  Neptune. — The  most  famous  example  of 
perturbations  is  found  in  connection  with  the  discovery, 
in  the  year  1846,  of  Neptune,  the  outermost  planet  of  the 
solar  system.  For  many  years  the  motion  of  Uranus,  his 
next  neighbor,  had  proved  a  puzzle  to  astronomers.  In 
accordance  with  Kepler's  first  law  this  planet  should  move 
in  an  ellipse  having  the  sun  at  one  of  its  foci,  but  no  ellipse 
could  be  found  which  exactly  fitted  its  observed  path  among 
the  stars,  although,  to  be  sure,  the  misfit  was  not  very  pro- 
nounced. Astronomers  surmised  that  the  small  deviations 
of  Uranus  from  the  best  path  which  theory  combined  with 
observation  could  assign,  were  due  to  perturbations  in  its 


64  ASTRONOMY 

motion  caused  by  an  unknown  planet  more  remote  from 
the  sun — a  thing  easy  to  conjecture  but  hard  to  prove,  and 
harder  still  to  find  the  unknown  disturber.  But  almost 
simultaneously  two  young  men,  Adams  in  England  and 
Le  Verrier  in  France,  attacked  the  problem  quite  inde- 
pendently of  each  other,  and  carried  it  to  a  successful  so- 
lution, showing  that  if  the  irregularities  in  the  motion  of 
Uranus  were  indeed  caused  by  an  unknown  planet,  then 
that  planet  must,  in  September,  1846,  be  in  the  direction 
of  the  constellation  Aquarius ;  and  there  it  was  found  on 
September  23d  by  the  astronomers  of  the  Berlin  Observatory 
whom  Le  Verrier  had  invited  to  search  for  it,  and  found 
within  a  degree  of  the  exact  point  which  the  law  of  gravi- 
tation in  his  hands  had  assigned  to  it. 

This  working  backward  from  the  perturbations  experi- 
enced by  Uranus  to  the  cause  which  produced  them  is  justly 
regarded  as  one  of  the  greatest  scientific  achievements  of 
the  human  intellect,  and  it  is  worthy  of  note  that  we  are 
approaching  the  time  at  which  it  may  be  repeated,  for  Nep- 
tune now  behaves  much  as  did  Uranus  three  quarters  of  a 
century  ago,  and  the  most  plausible  explanation  which  can 
be  offered  for  these  anomalies  in  its  path  is  that  the  bounds 
of  the  solar  system  must  be  again  enlarged  to  include  an- 
other disturbing  planet. 

42.  The  shape  of  a  planet, — There  is  an  effect  of  gravita- 
tion not  yet  touched  upon,  which  is  of  considerable  interest 
and  wide  application  in  astronomy — viz.,  its  influence  in  de- 
termining the  shape  of  the  heavenly  bodies.  The  earth  is 
a  globe  because  every  part  of  it  is  drawn  toward  the  center 
by  the  attraction  of  the  other  parts,  and  if  this  attraction 
on  its  surface  were  everywhere  of  equal  force  the  material 
of  the  earth  would  be  crushed  by  it  into  a  truly  spherical 
form,  no  matter  what  may  have  been  the  shape  in  which  it 
was  originally  made.  But  such  is  not  the  real  condition  of 
the  earth,  for  its  diurnal  rotation  develops  in  every  particle 
of  its  body  a  force  which  is  sometimes  called  centrifugal, 


CELESTIAL  MECHANICS  65 

but  which  is  really  nothing  more  than  the  inertia  of  its 
particles,  which  tend  at  every  moment  to  keep  unchanged 
the  direction  of  their  motion  and  which  thus  resist  the  at- 
traction that  pulls  them  into  a  circular  path  marked  out 
by  the  earth's  rotation,  just  as  a  stone  tied  at  the  end  of 
a  string  and  swung  swiftly  in  a  circle  pulls  upon  the 
string  and  opposes  the  constraint  which  keeps  it  moving 
in  a  circle.  A  few  experiments  with  such  a  stone  will 
show  that  the  faster  it  goes  the  harder  does  it  pull  upon 
the  string,  and  the  same  is  true  of  each  particle  of  the 
earth,  the  swiftly  moving  ones  near  the  equator  having 
a  greater  centrifugal  force  than  the  slow  ones  near  the 
poles.  .  At  the  equator  the  centrifugal  force  is  directly 
opposed  to  the  force  of  gravity,  and  in  effect  diminishes  it, 
so  that,  comparatively,  there  is  an  excess  of  gravity  at  the 
poles  which  compresses  the  earth  along  its  axis  and  causes 
it  to  bulge  out  at  the  equator  until  a  balance  is  thus  re- 
stored. As  we  have  learned  from  the  study  of  geography, 
in  the  case  of  the  earth,  this  compression  amounts  to  about 
27  miles,  but  in  the  larger  planets,  Jupiter  and  Saturn,  it 
is  much  greater,  amounting  to  several  thousand  miles. 

But  rotation  is  not  the  only  influence  that  tends  to 
pull  a  planet  out  of  shape.  The  attraction  which  the  earth 
exerts  upon  the  moon  is  stronger  on  the  near  side  and 
weaker  on  the  far  side  of  our  satellite  than  at  its  center, 
and  this  difference  of  attraction  tends  to  warp  the  moon,  as 
is  illustrated  in  Fig.  23  where  ./,  #,  and  8  represent  pieces 
of  iron  of  equal  mass  placed  in  line  on  a  table  near  a  horse- 
shoe magnet,  H.  Each  piece  of  iron  is  attracted  by  the 
magnet  and  is  held  back  by  a  weight  to  which  it  is 
fastened  by  means  of  a  cord  running  over  a  pulley,  P, 
at  the  edge  of  the  table.  These  weights  are  all  to  be 
supposed  equally  heavy  and  each  of  them  pulls  upon  its 
piece  of  iron  with  a  force  just  sufficient  to  balance  the 
attraction  of  the  magnet  for  the  middle  piece,  No.  2. 
It  is  clear  that  under  this  arrangement  No.  2  will  move 


66 


ASTRONOMY 


neither  to  the  right  nor  to  the  left,  since  the  forces  exerted 
upon  it  by  the  magnet  and  the  weight  just  balance  each 
other.  Upon  No.  1,  however,  the  magnet  pulls  harder 
than  upon  No.  #,  because  it  is  nearer  and  its  pull  there- 


FIG.  23. — Tide-raising  forces. 

fore  more  than  balances  the  force  exerted  by  the  weight, 
so  that  No.  1  will  be  pulled  away,  from  No.  2  and  will 
stretch  the  elastic  cords,  which  are  represented  by  the 
lines  joining  1  and  #,  until  their  tension,  together  with  the 
force  exerted  by  the  weight,  just  balances  the  attraction 
of  the  magnet.  For  No.  8,  the  force  exerted  by  the  magnet 
is  less  than  that  of  the  weight,  and  it  will  also  be  pulled 
away  from  No.  2  until  its  elastic  cords  are  stretched  to  the 
proper  tension.  The  net  result  is  that  the  three  blocks 
which,  without  the  magnet's  influence,  would  be  held  close 
together  by  the  elastic  cords,  are  pulled  apart  by  this  out- 
side force  as  far  as  the  resistance  of  the  cords  will  permit. 
An  entirely  analogous  set  of  forces  produces  a  similar 
effect  upon  the  shape  of  the  moon.  The  elastic  cords  of 
Fig.  23  stand  for  the  attraction  of  gravitation  by  which  all 
the  parts  of  the  moon  are  bound  together.  The  magnet 
represents  the  earth  pulling  with  unequal  force  upon  differ- 
ent parts  of  the  moon.  The  weights  are  the  inertia  of  the 
moon  in  its  orbital  motion  which,  as  we  have  seen  in  a 


CELESTIAL   MECHANICS 


67 


previous  section,  upon  the  whole  just  balances  the  earth's 
attraction  and  keeps  the  moon  from  falling  into  it.  The 
effect  of  these  forces  is  to  stretch  out  the  moon  along  a  line 
pointing  toward  the  earth,  just  as  the  blocks  were  stretched 
out  along  the  line  of  the  magnet,  and  to  make  this  diam- 
eter of  the  moon  slightly  but  permanently  longer  than 
the  others. 

The  tides. — Similarly  the  moon  and  the  sun  attract  op- 
posite sides  of  the  earth  with  different  forces  and  feebly 
tend  to  pull  it  out  of  shape.  But  here 
a  new  element  comes  into  play :  the 
earth  turns  so  rapidly  upon  its  axis 
that  its  solid  parts  have  no  time  in 
which  to  yield  sensibly  to  the  strains, 
which  shift  rapidly  from  one  diameter 
to  another  as  different  parts  of  the 
earth  are  turned  toward  the  moon,  and 
it  is  chiefly  the  waters  of  the  sea  which 
respond  to  the  distorting  effect  of  the 
sun's  and  moon's  attraction.  These  are 
heaped  up  on  opposite  sides  of  the 
earth  so  as  to  produce  a  slight  elonga- 
tion of  its  diameter,  and  Fig.  24  shows 
how  by  the  earth's  rotation  this  swell- 
ing of  the  waters  is  swept  out  from 
under  the  moon  and  is  pulled  back  by 
the  moon  until  it  finally  takes  up  some 
such  position  as  that  shown  in  the  fig- 
ure where  the  effect  of  the  earth's  rota- 
tion in  carrying  it  one  way  is  just  bal- 
anced by  the  moon's  attraction  urging 
it  back  on  line  with  the  moon.  This  heaping  up  of  the 
waters  is  called  a  tide.  If  /in  the  figure  represents  a  little 
island  in  the  sea  the  waters  which  surround  it  will  of 
course  accompany  it  in  its  diurnal  rotation  about  the 
earth's  axis,  but  whenever  the  island  comes  back  to  the 


FIG.  24.— The  tides. 


68  ASTRONOMY 

position  /,  the  waters  will  swell  up  as  a  part  of  the  tidal 
wave  and  will  encroach  upon  the  land  in  what  is  called 
high  tide  or  flood  tide.  So  too  when  they  reach  7",  half  a 
day  later,  they  will  again  rise  in  flood  tide,  and  midway 
between  these  points,  at  /',  the  waters  must  subside,  giv- 
ing low  or  ebb  tide. 

The  height  of  the  tide  raised  by  the  moon  in  the  open 
sea  is  only  a  very  few  feet,  and  the  tide  raised  by  the  sun  is 
even  less,  but  along  the  coast  of  a  continent,  in  bays  and 
angles  of  the  shore,  it  often  happens  that  a  broad  but  low 
tidal  wave  is  forced  into  a  narrow  corner,  and  then  the  rise 
of  the  water  may  be  many  feet,  especially  when  the  solar 
tide  and  the  lunar  tide  come  in  together,  as  they  do  twice 
in  every  month,  at  new  and  full  moon.  Why  do  they  come 
together  at  these  times  instead  of  some  other  ? 

Small  as  are  these  tidal  effects,  it  is  worth  noting  that 
they  may  in  certain  cases  be  very  much  greater — e.  g.,  if 
the  moon  were  as  massive  as  is  the  sun  its  tidal  effect 
would  be  some  millions  of  times  greater  than  it  now  is  and 
would  suffice  to  grind  the  earth  into  fragments.  Although 
the  earth  escapes  this  fate,  some  other  bodies  are  not  so 
fortunate,  and  we  shall  see  in  later  chapters  some  evidence 
of  their  disintegration. 

43.  The  scope  of  the  law  of  gravitation.— In  all  the  do- 
main of  physical  science  there  is  no  other  law  so  famous  as 
the  Newtonian  law  of  gravitation  ;  none  other  that  has  been 
so  dwelt  upon,  studied,  and  elaborated  by  astronomers  and 
mathematicians,  and  perhaps  none  that  can  be  considered 
so  indisputably  proved.  Over  and  over  again  mathemat- 
ical analysis,  based  upon  this  law,  has  pointed  out  conclu- 
sions which,  though  hitherto  unsuspected,  have  afterward 
been  found  true,  as  when  Newton  himself  derived  as  a  corol- 
lary from  this  law  that  the  earth  ought  to  be  flattened  at 
the  poles — a  thing  not  known  at  that  time,  and  not  proved 
by  actual  measurement  until  long  afterward.  It  is,  in  fact, 
this  capacity  for  predicting  the  unknown  and  for  explain- 


CELESTIAL  MECHANICS  69 

ing  in  minutest  detail  the  complicated  phenomena  of  the 
heavens  and  the  earth  that  constitutes  the  real  proof  of  the 
law  of  gravitation,  and  it  is  therefore  worth  while  to  note 
that  at  the  present  time  there  are  a  very  few  points  at 
which  the  law  fails  to  furnish  a  satisfactory  account  of 
things  observed.  Chief  among  these  is  the  case  of  the  planet 
Mercury,  the  long  diameter  of  whose  orbit  is  slowly  turning 
around  in  a  way  for  which  the  law  of  gravitation  as  yet  fur- 
nishes no  explanation.  Whether  this  is  because  the  law  itself 
is  inaccurate  or  incomplete,  or  whether  it  only  marks  a  case 
in  which  astronomers  have  not  yet  properly  applied  the 
law  and  traced  out  its  consequences,  we  do  not  know  ;  but 
whether  it  be  the  one  or  the  other,  this  and  other  simila-r 
cases  show  that  even  here,  in  its  most  perfect  chapter, 
astronomy  still  remains  an  incomplete  science. 


CHAPTER  V 


THE   EARTH   AS  A  PLANET 

44.  The  size  of  the  earth, — The  student  is  presumed  to 
have  learned,  in  his  study  of  geography,  that  the  earth  is  a 
globe  about  8,000  miles  in  diameter  and,  without  dwelling 
upon  the  "  proofs  "  which  are  commonly  given  for  these 
statements,  we  proceed  to  consider  the  principles  upon 

which  the  measurement  of 
the  earth's  size  and  shape 
are  based. 

In  Fig.  25  the  circle  rep- 
resents a  meridian  section 
of  the  earth ;  P  P'  is  the 
axis  about  which  it  rotates, 
and  the  dotted  lines  repre- 
sent a  beam  of  light  com- 
ing from  a  star  in  the  plane 
of  the  meridian,  and  so  dis- 
tant that  the  dotted  lines 
are  all  practically  parallel 

Pio.  25,-Measuring  the  size  of  the  earth.    ^  ^  ^^       ^  ^^ 

radii  drawn  through  the  points  -/,  #,  #,  represent  the  direc- 
tion of  the  vertical  at  these  points,  and  the  angles  which 
these  radii  produced,  make  with  the  rays  of  starlight  are 
each  equal  to  the  angular  distance  of  the  star  from  the 
zenith  of  the  place  at  the  moment  the  star  crosses  the  me- 
ridian. We  have  already  seen,  in  Chapter  II,  how  these 
angles  may  be  measured,  and  it  is  apparent  from  the  figure 
that  the  difference  between  any  two  of  these  angles — e.  g., 
70 


THE  EARTH  AS  A  PLANET  71 

the  angles  at  1  and  2 — is  equal  to  the  angle  at  the  center, 
0,  between  the  points  1  and  2.  By  measuring  these  angu- 
lar distances  of  the  star  from  the  zenith,  the  astronomer 
finds  the  angles  at  the  center  of  the  earth  between  the  sta- 
tions 1,  2,  3,  etc.,  at  which  his  observations  are  made.  If 
the  meridian  were  a  perfect  circle  the  change  of  zenith  dis- 
tance of  the  star,  as  one  traveled  along  a  meridian  from  the 
equator  to  the  pole,  would  be  perfectly  uniform — the  same 
number  of  degrees  for  each  hundred  miles  traveled — and 
observations  made  in  many  parts  of  the  earth  show  that 
this  is  very  nearly  true,  but  that,  on  the  whole,  as  we  ap- 
proach the  pole  it  is  necessary  to  travel  a  little  greater  dis- 
tance than  is  required  for  a  given  change  in  the  angle  at 
the  equator.  The  earth  is,  in  fact,  flattened  at  the  poles  to 
the  amount  of  about  27  miles  in  the  length  of  its  diameter, 
and  by  this  -amount,  as  well  as  by  smaller  variations  due  to 
mountains  and  valleys,  the  shape  of  the  earth  differs  from 
a  perfect  sphere.  These  astronomical  measurements  of  the 
curvature  of  the  earth's  surface  furnish  by  far  the  most  sat- 
isfactory proof  that  it  is  very  approximately  a  sphere,  and 
furnish  as  its  equatorial  diameter  7,926  miles. 

Neglecting  ths  compression,  as  it  is  called,  i.  e.,  the  27 
miles  by  which  the  equatorial  diameter  exceeds  the  polar, 
the  size  of  the  earth  may  easily  be  found  by  measuring  the 
distance  1  —  2  along  the  surface  and  by  combining  with  this 
the  angle  102  obtained  through  measuring  the  meridian 
altitudes  of  any  star  as  seen  from  1  and  2.  Draw  on  paper 
an  angle  equal  to  the  measured  difference  of  altitude  and 
find  how  far  you  must  go  from  its  vertex  in  order  to  have 
the  distance  between  the  sides,  measured  along  an  arc  of 
a  circle,  equal  to  the  measured  distance  between  1  and  2. 
This  distance  from  the  vertex  will  be  the  earth's  radius. 

EXERCISE  19. — Measure  the  diameter  of  the  earth  by 
the  method  given  above.  In  order  that  this  may  be  done 
satisfactorily,  the  two  stations  at  which  observations  are 
made  must  be  separated  by  a  considerable  distance — i.  e., 


ASTBONOMY 


200  miles.  They  need  not  be  on  the  same  meridian,  but  if 
they  are  on  different  meridians  in  place  of  the  actual  dis- 
tance between  them,  there  must  be  used  the  projection  of 
that  distance  upon  the  meridian — i.  e.,  the  north  and  south 
part  of  the  distance. 

By  co-operation  between  schools  in  the  Northern  and 
Southern  States,  using  a  good  map  to  obtain  the  required 
distances,  the  diameter  of  the  earth 
may  be  measured  with  the  plumb- 
line  apparatus  described  in  Chapter 
II  and  determined  within  a  small 
percentage  of  its  true  value. 

45.  The  mass  of  the  earth.— We 
have  seen  in  Chapter  IV  the  possi- 
bility of  determining  the  masses  of 
the  planets  as  fractional  parts  of 
the  sun's  mass,  but  nothing  was 
there  shown,  or  could  be  shown, 
about  measuring  these  masses  after 
the  common  fashion  in  kilogrammes 
or  tons.  To  do  this  we  must  first 
get  the  mass  of  the  earth  in  tons  or 
kilogrammes,  and  while  the  princi- 
ples involved  in  this  determination 
are  simple  enough,  their  actual  ap- 
.  26. -illustrating  the  prin-  plication  is  delicate  and  difficult. 

In  Fig.  26  we  suppose  a  long 
plumb  line  to  be  suspended  above 
the  surface  of  the  earth  and  to  be  attracted  toward  the 
center  of  the  earth,  (7,  by  a  force  whose  intensity  is  (Chap- 
ter IV) 


1C 


ciples  involved  in  weighing 
the  earth. 


where  E  denotes  the  mass  of  the  earth,  which  is  to  be  de- 
termined by  experiment,  and  R  is  the  radius  of  the  earth, 
3,963  miles.  If  there  is  no  disturbing  influence  present, 


THE  EARTH  AS  A   PLANET  73 

the  plumb  line  will  point  directly  downward,  but  if  a  mas- 
sive ball  of  lead  or  other  heavy  substance  is  placed  at  one 
side,  ^,  it  will  attract  the  plumb  line  with  a  force  equal  to 

/  =  k  m^  , 

where  r  is  the  distance  of  its  center  from  the  plumb  bob 
and  B  is  its  mass  which  we  may  suppose,  for  illustration, 
to  be  a  ton.  In  consequence  of  this  attraction  the  plumb 
line  will  be  pulled  a  little  to  one  side,  as  shown  by  the  dot- 
ted line,  and  if  we  represent  by  I  the  length  of  the  plumb 
line  and  by  d  the  distance  between  the  original  and  the 
disturbed  positions  of  the  plumb  bob  we  may  write  the  pro- 
portion 

and  introducing  the  values  of  F  and  /  given  above,  and 
solving  for  J^the  proportion  thus  transformed,  we  find 

T7T  ~D        v        /    -iV 

J]j    =T    £}   .  —   . 

d  \  T 

In  this  equation  the  mass  of  the  ball,  B,  the  length  of  the 
plumb  line,  I,  the  distance  between  the  center  of  the  ball 
and  the  center  of  the  plumb  bob,  r,  and  the  radius  of  the 
earth,  R,  can  all  be  measured  directly,  and  d,  the  amount 
by  which  the  plumb  bob  is  pulled  to  one  side  by  the  ball,  is 
readily  found  by  shifting  the  ball  over  to  the  other  side,  at 
2)  and  measuring  with  a  microscope  how  far  the  plumb 
bob  moves.  This  distance  will,  of  course,  be  equal  to  2  d. 

By  methods  involving  these  principles,  but  applied  in  a 
manner  more  complicated  as  well  as  more  precise,  the  mass 
of  the  earth  is  found  to  be,  in  tons,  6,642  X  1018 — i.  e.,  6,642 
followed  by  18  ciphers,  or  in  kilogrammes  60,258  X  1020. 
The  earth's  atmosphere  makes  up  about  a  millionth  part 
of  this  mass. 

If  the  length  of  the  plumb  line  were  100  feet,  the 
weight  of  the  ball  a  ton,  and  the  distance  between  the  two 
6 


74  ASTRONOMY 

positions  of  the  ball,  1  and  #,  six  feet,  how  many  inches,  d, 
would  the  plumb  bob  be  pulled  out  of  place  ? 

Find  from  the  mass  of  the  earth  and  the  data  of  §  40 
the  mass  of  the  sun  in  tons.  Find  also  the  mass  of  Mars. 
The  computation  can  be  very  greatly  abridged  by  the  use 
of  logarithms. 

46.  Precession,— That  the  earth  is  isolated  in  space  and 
has  no  support  upon  which  to  rest,  is  sufficiently  shown  by 
the  fact  that  the  stars  are  visible  upon  every  side  of  it,  and 
no  support  can  be  seen  stretching  out  toward  them.  We 
must  then  consider  the  earth  to  be  a  globe  traveling  freely 
about  the  sun  in  a  circuit  which  it  completes  once  every 
year,  and  rotating  once  in  every  twenty-four  hours  about 
an  axis  which  remains  at  all  seasons  directed  very  nearly 
toward  the  star  Polaris.  The  student  should  be  able  to 
show  from  his  own  observations  of  the  sun  that,  with  refer- 
ence to  the  stars,  the  direction  of  the  sun  from  the  earth 
changes  about  a  degree  a  day.  Does  this  prove  that  the 
earth  revolves  about  the  sun  ? 

But  it  is  only  in  appearance  that  the  pole  maintains  its 
fixed  position  among  the  stars.  If  photographs  are  taken 
year  after  year,  after  the  manner  of  Exercise  7,  it  will  be 
found  that  slowly  the  pole  is  moving  (nearly)  toward  Po- 
laris, and  making  this  star  describe  a  smaller  and  smaller 
circle  in  its  diurnal  path,  while  stars  on  the  other  side  of 
the  pole  (in  right  ascension  12h.)  become  more  distant 
from  it  and  describe  larger  circles  in  their  diurnal  motion  ; 
but  the  process  takes  place  so  slowly  that  the  space  of  a 
lifetime  is  required  for  the  motion  of  the  pole  to  equal  the 
angular  diameter  of  the  full  moon. 

Spin  a  top  and  note  how  its  rapid  whirl  about  its  axis 
corresponds  to  the  earth's  diurnal  rotation.  When  the  axis 
about  which  the  top  spins  is  truly  vertical  the  top  "  sleeps  " ; 
but  if  the  axis  is  tipped  ever  so  little  away  from  the  verti- 
cal it  begins  to  wabble,  so  that  if  we  imagine  the  axis  pro- 
longed out  to  the  sky  and  provided  with  a  pencil  point  as 


THE  EARTH   AS  A  PLANET  75 

a  marker,  this  would  trace  a  circle  around  the  zenith,  along 
which  the  pole  of  the  top  would  move,  and  a  little  observa- 
tion will  show  that  the  more  the  top  is  tipped  from  the 
vertical  the  larger  does  this  circle  become  and  the  more 
rapidly  does  the  wabbling  take  place.  Were  it  not  for  the 
spinning  of  the  top  about  its  axis,  it  would  promptly  fall 
over  when  tipped  from  the  vertical  position,  but  the  spin 
combines  with  the  force  which  pulls  the  top  over  and  pro- 
duces the  wabbling  motion.  Spin  the  top  in  opposite 
directions,  with  the  hands  of  a  watch  and  contrary  to  the 
hands  of  a  watch,  and  note  the  effect  which  is  produced 
upon  the  wabbling. 

The  earth  presents  many  points  of  resemblance  to  the 
top.  Its  diurnal  rotation  is  the  spin  about  the  axis.  This 
axis  is  tipped  23.5°  away  frojn  the  perpendicular  to  its 
orbit  (obliquity  of  the  ecliptic)  just  as  the  axis  of  the  top 
is  tipped  away  from  the  vertical  line.  In  consequence  of 
its  rapid  spin,  the  body  of  the  earth  bulges  out  at  the  equa- 
tor (27  miles),  and  the  sun  and  moon,  by  virtue  of  their  at- 
traction (see  Chapter  IV),  lay  hold  of  this  protuberance  and 
pull  it  down  toward  the  plane  of  the  earth's  orbit,  so  that  if 
it  were  not  for  the  spin  this  force  would  straighten  the  axis 
up  and  set  it  perpendicular  to  the  orbit  plane.  But  here,  as 
in  the  case  of  the  top,  the  spin  and  the  tipping  force  com- 
bine to  produce  a  wabble  which  is  called  precession,  and 
whose  effect  we  recognize  in  the  shifting  position  of  the 
pole  among  the  stars.  The  motion  of  precession  is  very 
much  slower  than  the  wabbling  of  the  top,  since  the  tip- 
ping force  for  the  earth  is  relatively  very  small,  and  a  pe- 
riod of  nearly  26,000  years  is  required  for  a  complete  cir- 
cuit of  the  pole  about  its  center  of  motion.  Friction  ulti- 
mately stops  both  the  spin  and  the  wabble  of  the  top,  but 
this  influence  seems  wholly  absent  in  the  case  of  the  earth, 
and  both  rotation  and  precession  go  on  unchanged  from 
century  to  century,  save  for  certain  minor  forces  which  for 
a  time  change  the  direction  or  rate  of  the  precessional 


76  ASTRONOMY 

motion,  first  in  one  way  and  then  in  another,  without  in 
the  long  run  producing  any  results  of  consequence. 

The  center  of  motion,  about  which  the  pole  travels  in  a 
small  circle  having  an  angular  radius  of  23.5°,  is  at  that 
point  of  the  heavens  toward  which  a  perpendicular  to  the 
plane  of  the  earth's  orbit  points,  and  may  be  found  on  the 
star  map  in  right  ascension  18h.  Om.  and  declination  66.5°. 

EXERCISE  20. — Find  this  point  on  the  map,  and  draw 
as  well  as  you  can  the  path  of  the  pole  about  it.  The  mo- 
tion of  the  pole  along  its  path  is  toward  the  constellation 
Cepheus.  Mark  the  position  of  the  pole  along  this  path 
at  intervals  of  1,000  years,  and  refer  to  these  positions  in 
dealing  with  some  of  the  following  questions  : 

Does  the  wabbling  of  the  top  occur  in  the  same  direc- 
tion as  the  motion  of  precession  ?  Do  the  tipping  forces 
applied  to  the  earth  and  top  act  in  the  same  direction  ? 
What  will  be  the  polar  star  12,000  years  hence?  The 
Great  Pyramid  of  Egypt  is  thought  to  have  been  used 
as  an  observatory  when  Alpha  Draconis  was  the  bright  star 
nearest  the  pole.  How  long  ago  was  that  ? 

The  motion  of  the  pole  of  course  carries  the  equator 
and  the  equinoxes  with  it,  and  thus  slowly  changes  the 
right  ascensions  and  declinations  of  all  the  stars.  On  this 
account  it  is  frequently  called  the  precession  of  the  equi- 
noxes, and  this  motion  of  the  equinox,  slow  though  it  is, 
is  a  matter  of  some  consequence  in  connection  with  chro- 
nology and  the  length  of  the  year. 

Will  the  precession  ever  bring  back  the  right  ascen- 
sions and  declinations  to  be  again  what  they  now  are  ? 

In  what  direction  is  the  pole  moving  with  respect  to 
the  Big  Dipper  ?  Will  its  motion  ever  bring  it  exactly  to 
Polaris  ?  How  far  away  from  Polaris  will  the  precession 
carry  the  pole  ?  What  other  bright  stars  will  be  brought 
near  the  pole  by  the  precession  ? 

47.  The  warming  of  the  earth. — Winter  and  summer  alike 
the  day  is  on  the  average  warmer  than  the  night,  and  it  is 


THE  EARTH  AS  A  PLANET  ff 

easy  to  see  that  this  surplus  of  heat  comes  from  the  sun  by 
day  and  is  lost  by  night  through  radiation  into  the  void 
which  surrounds  the  earth ;  just  as  the  heat  contained  in  a 
mass  of  molten  iron  is  radiated  away  and  the  iron  cooled 
when  it  is  taken  out  from  the  furnace  and  placed  amid 
colder  surroundings.  The  earth's  loss  of  heat  by  radiation 
goes  on  ceaselessly  day  and  night,  and  were  it  not  for  the 
influx  of  solar  heat  this  radiation  would  steadily  diminish 
the  temperature  toward  what  is  called  the  "  absolute  zero  " 
— i.  e.,  a  state  in  which  all  heat  has  been  taken  away  and 
beyond  which  there  can  be  no  greater  degree  of  cold.  This 
must  not  be  confounded  with  the  zero  temperatures  shown 
by  our  thermometers,  since  it  lies  nearly  500°  below  the  zero 
of  the  Fahrenheit  scale  (—273°  Centigrade),  a  temperature 
which  by  comparison  makes  the  coldest  winter  weather 
seem  warm,  although  the  ordinary  thermometer  may  regis- 
ter many  degrees  below  its  zero.  The  heat  radiated  by  the 
sun  into  the  surrounding  space  on  every  side  of  it  is  another 
example  of  the  same  cooling  process,  a  hot  body  giving  up 
its  hea.t  to  the  colder  space  about  it,  and  it  is  the  minute 
fraction  of  this  heat  poured  out  by  the  sun,  and  in  small 
part  intercepted  by  the  earth,  which  warms  the  latter  and 
produces  what  we  call  weather,  climate,  the  seasons,  etc. 

Observe  the  fluctuations,  the  ebb  and  flow,  which  are 
inherent  in  this  process.  From  sunset  to  sunrise  there  is 
nothing  to  compensate  the  steady  outflow  of  heat,  and 
air  and  ground  grow  steadily  colder,  but  with  the  sunrise 
there  comes  an  influx  of  solar  heat,  feeble  at  first'  because 
it  strikes  the  earth's  surface  very  obliquely,  but  becoming 
more  and  more  efficient  as  the  sun  rises  higher  in  the  sky. 
But  as  the  air  and  the  ground  grow  warm  during  the  morn- 
ing hours  they  part  more  and  more  readily  and  rapidly  with 
their  store  of  heat,  just  as  a  steam  pipe  or  a  cup  of  coffee 
radiates  heat  more  rapidly  when  very  hot.  The  warmest 
hour  of  the  day  is  reached  when  these  opposing  tendencies 
of  income  and  expenditure  of  heat  are  just  balanced ;  and 


78  ASTRONOMY 

barring  such  disturbing  factors  as  wind  and  clouds,  the  gain 
in  temperature  usually  extends  to  the  time — an  hour  or  two 
beyond  noon — at  which  the  diminishing  altitude  of  the  sun 
renders  his  rays  less  efficient,  when  radiation  gains  the 
upper  hand  and  the  temperature  becomes  for  a  short  time 
stationary,  and  then  commences  to  fall  steadily  until  the 
next  sunrise. 

We  have  here  an  example  of  what  is  called  a  periodic 
change — i.  e.,  one  which,  within  a  definite  and  uniform 
period  (24  hours),  oscillates  from  a  minimum  up  to  a 
maximum  temperature  and  then  back  again  to  a  minimum, 
repeating  substantially  the  same  variation  day  after  day. 
But  it  must  be  understood  that  minor  causes  not  taken 
into  account  above,  such  as  winds,  water,  etc.,  produce 
other  fluctuations  from  day  to  day  which  sometimes  ob- 
scure or  even  obliterate  the  diurnal  variation  of  tempera- 
ture caused  by  the  sun. 

Expose  the  back  of  your  hand  to  the  sun,  holding  the 
hand  in  such  a  position  that  the  sunlight  strikes  perpen- 
dicularly upon  it;  then  turn  the  hand  so  that  the  light 
falls  quite  obliquely  upon  it  and  note  how  much  more  vig- 
orous is  the  warming  effect  of  the  sun  in  the  first  position 
than  in  the  second.  It  is  chiefly  this  difference  of  angle 
that  makes  the  sun's  warmth  more  effective  when  he  is 
high  up  in  the  sky  than  when  he  is  near  the  horizon,  and 
more  effective  in  summer  than  in  winter. 

We  have  seen  in  Chapter  III  that  the  sun's  motion 
among  the  stars  takes  place  along  a  path  which  carries  it 
alternately  north  and  south  of  the  equator  to  a  distance 
of  23.5°,  and  the  stars  show  by  their  earlier  risings  and 
later  settings,  as  we  pass  from  the  equator  toward  the 
north  pole  of  the  heavens,  that  as  the  sun  moves  north- 
ward from  the  equator,  each  day  in  the  northern  hemi- 
sphere will  become  a  little  longer,  each  night  a  little  shorter, 
and  every  day  the  sun  will  rise  higher  toward  the  zenith 
until  this  process  culminates  toward  the  end  of  June,  when 


THE  EARTH  AS  A  PLANET  79 

the  sun  begins  to  move  southward,  bringing  shorter  days 
and  smaller  altitudes  until  the  Christmas  season,  when 
again  it  is  reversed  and  the  sun  moves  northward.  "We 
have  here  another  periodic  variation,  which  runs  its  com- 
plete course  in  a  period  of  a  year,  and  it  is  easy  to  see  that 
this  variation  must  have  a  marked  effect  on  the  warming 
of  the  earth,  the  long  days  and  great  altitudes  of  summer 
producing  the  greater  warmth  of  that  season,  while  the 
shorter  days  and  lower  altitudes  of  December,  by  diminish- 
ing the  daily  supply  of  solar  heat,  bring  on  the  winter's 
cold.  The  succession  of  the  seasons,  winter  following  sum- 
mer and  summer  winter,  is  caused  by  the  varying  altitude 
of  the  sun,  and  this  in  turn  is  due  to  the  obliquity  of  the 
ecliptic,  or,  what  is  the  same  thing,  the  amount  by  which 
the  axis  of  the  earth  is  tipped  from  being  perpendicular  to 
the  plane  of  its  orbit,  and  the  seasons  are  simply  a  periodic 
change  in  the  warming  of  the  earth,  quite  comparable  with 
the  diurnal  change  but  of  longer  period. 

It  is  evident  that  the  period  within  which  the  succession 
of  winter  and  summer  is  completed,  the  year,  as  we  com- 
monly call  it,  must  equal  the  time  required  by  the  sun  to 
go  from  the  vernal  equinox  around  to  the  vernal  equinox 
again,  since  this  furnishes  a  complete  cycle  of  the  sun's 
motions  north  and  south  from  the  equator.  On  account 
of  the  westward  motion  of  the  equinox  (precession)  this 
is  not  quite  the  same  as  the  time  required  for  a  com- 
plete revolution  of  the  earth  in  its  orbit,  but  is  a  little 
shorter  (20m.  23s.),  since  the  equinox  moves  back  to  meet 
the  sun. 

48.  Relation  of  the  sun  to  climate,— It  is  clear  that  both 
the  northern  and  southern  hemispheres  of  the  earth  must 
have  substantially  the  same  kind  of  seasons,  since  the  mo- 
tion of  the  sun  north  and  south  affects  both  alike ;  but 
when  the  sun  is  north  of  the  equator  and  warming  our 
hemisphere  most  effectively,  his  light  falls  more  obliquely 
upon  the  other  hemisphere,  the  days  there  are  short  and 


80  ASTRONOMY 

winter  reigns  at  the  time  we  are  enjoying  summer,  while 
six  months  later  the  conditions  are  reversed. 

In  those  parts  of  the  earth  near  the  equator — the  torrid 
zone  —there  is  no  such  marked  change  from  cold  to  warm 
as  we  experience,  because,  as  the  sun  never  gets  more  than 
23.5°  away  from  the  celestial  equator,  on  every  day  of  the 
year  he  mounts  high  in  the  tropic  skies,  always  coming 
within  23.5°  of  the  zenith,  and  usually  closer  than  this,  so 
that  there  is  no  such  periodic  change  in  the  heat  supply  as 
is  experienced  in  higher  latitudes,  and  within  the  tropics 
the  temperature  is  therefore  both  higher  and  more  uniform 
than  in  our  latitude. 

In  the  frigid  zones,  on  the  contrary,  the  sun  never  rises 
high  in  the  sky ;  at  the  poles  his  greatest  altitude  is  only 
23.5°,  and  during  the  winter  season  he  does  not  rise  at  all, 
so  that  the  temperature  is  here  low  the  whole  year  round, 
and  during  the  winter  season,  when  for  weeks  or  months  at 
a  time  the  supply  of  solar  light  is  entirely  cut  off,  the  tem- 
perature falls  to  a  degree  unknown  in  more  favored  climes. 

If  the  obliquity  of  the  ecliptic  were  made  10°  greater, 
what  would  be  the  effect  upon  the  seasons  in  the  temperate 
zones  ?  What  if  it  were  made  10°  less  ? 

Does  the  precession  of  the  equinoxes  have  any  effect 
upon  the  seasons  or  upon  the  climate  of  different  parts  of 
the  earth  ? 

If  the  axis  of  the  earth  pointed  toward  Arcturus  instead 
of  Polaris,  would  the  seasons  be  any  different  from  what 
they  are  now  ? 

49.  The  atmosphere. — Although  we  live  upon  its  surface, 
we  are  not  outside  the  earth,  but  at  the  bottom  of  a  sea  of 
air  which  forms  the  earth's  outermost  layer  and  extends 
above  our  heads  to  a  height  of  many  miles.  The  study  of 
most  of  the  phenomena  of  the  atmosphere  belongs  to  that 
branch  of  physics  called  meteorology,  but  there  are  a  few 
matters  which  fairly  come  within  oar  consideration  of  the 
earth  as  a  planet. 


THE   EARTH  AS  A  PLANET  81 

We  can  not  see  the  stars  save  as  we  look  through  this 
atmosphere,  and  the  light  which  comes  through  it  is  bent 
and  oftentimes  distorted  so  as  to  present  serious  obstacles 
to  any  accurate  telescopic  study  of  the  heavenly  bodies. 
Frequently  this  disturbance  is  visible  to  the  naked  eye,  and 
the  stars  are  said  to  twinkle — i.  e.,  to  quiver  and  change 
color  many  times  per  second,  solely  in  consequence  of  a  dis- 
turbed condition  of  the  air  and  not  from  anything  which 
goes  on  in  the  star.  This  effect  is  more  marked  low  down 
in  the  sky  than  near  the  zenith,  and  it  is  worth  noting  that 
the  planets  show  very  little  of  it  because  the  light  they 
send  to  the  earth  comes  from  a  disk  of  sensible  area,  while 
a  star,  being  much  smaller  and  farther  from  the  earth,  has 
its  disk  reduced  practically  to  a  mere  point  whose  light  is 
more  easily  affected  by  local  disturbances  in  the  atmosphere 
than  is  the  broader  beam  which  comes  from  the  planets' 
disk. 

50.  Refraction. — At  all  times,  whether  the  stars  twinkle 
or  not,  their  light  is  bent  in  its  passage  through  the  atmos- 
phere, so  that  the  stars  appear  to  stand  higher  up  in  the 
sky  than  their  true  positions.  This  effect,  which  the  as- 
tronomer calls  refraction,  must  be  allowed  for  in  observa- 
tions of  the  more  precise  class,  although  save  at  low  alti- 
tudes its  amount  is  a  very  small  fraction  of  a  degree,  but 
near  the  horizon  it  is  much  exaggerated  in  amount  and 
becomes  easily  visible  to  the  naked  eye  by  distorting  the 
disks  of  the  sun  and  moon  from  circles  into  ovals  with 
their  long  diameters  horizontal.  The  refraction  lifts  both 
upper  and  lower  edge  of  the  sun,  but  lifts  the  lower  edge 
more  than  the  upper,  thus  shortening  the  vertical  diameter. 
See  Fig.  27,  which  shows  not  only  this  effect,  but  also  the 
reflection  of  the  sun  from  the  curved  surface  of  the  sea, 
still  further  flattening  the  image.  If  the  surface  of  the 
water  were  flat,  the  reflected  image  would  have  the  same 
shape  as  the  sun's  disk,  and  its  altered  appearance  is  some- 
times cited  as  a  proof  that  the  earth's  surface  is  curved. 


82 


ASTRONOMY 


The  total  amount  of  the  refraction  at  the  horizon  is  a 
little  more  than  half  a  degree,  and  since  the  diameters  of 
the  sun  and  moon  subtend  an  angle  of  about  half  a  degree, 
we  have  the  remarkable  result  that  in  reality  the  whole 


BF 


FIG.  2?.— Flattening  of  the  sun's  disk  by  refraction  and  by  reflection  from  the 
surface  of  the  sea. 

disk  of  either  sun  or  moon  is  below  the  horizon  at  the 
instant  that  the  lower  edge  appears  to  touch  the  horizon 
and  sunset  or  moonset  begins.  The  same  effect  exists  at 
sunrise,  and  as  a  consequence  the  duration  of  sunshine  or 
of  moonshine  is  on  the  average  about  six  minutes  longer 
each  day  than  it  would  be  if  there  were  no  atmosphere  and 
no  refraction.  A  partial  offset  to  this  benefit  is  found  in 
the  fact  that  the  atmosphere  absorbs  the  light  of  the  heav- 
enly bodies,  so  that  stars  appear  much  less  bright  when 
near  the  horizon  than  when  they  are  higher  up  in  the  sky, 
and  by  reason  of  this  absorption  the  setting  sun  can  be 
looked  at  with  the  naked  eye  without  the  discomfort  which 
its  dazzling  luster  causes  at  noon. 

51.  The  twilight.— Another   effect  of  the  atmosphere, 
even  more  marked  than  the  preceding,  is  the  twilight.     As 


THE  EARTH  AS  A  PLANET  83 

at  sunrise  the  mountain  top  catches  the  rays  of  the  coming 
sun  before  they  reach  the  lowland,  and  at  sunset  it  keeps 
them  after  they  have  faded  from  the  regions  below,  so  the 
particles  of  dust  and  vapor,  which  always  float  in  the  atmos- 
phere, catch  the  sunlight  and  reflect  it  to  the  surface  of  the 
earth  while  the  sun  is  still  below  the  horizon,  giving  at  the 
beginning  and  end  of  day  that  vague  and  diffuse  light  which 
we  call  twilight. 

Fig.  28  shows  a  part  of  the  earth  surrounded  by  such  a 
dust-laden  atmosphere,  which  is  illuminated  on  the  left  by 
the  rays  of  the  sun,  but  which,  on  the  right  of  the  figure, 
lies  in  the  shadow  cast 
by  the  earth.  To  an 
observer  placed  at  1  the 
sun  is  just  setting,  and 
all  the  atmosphere 
above 'him  is  illumined 
with  its  rays,  which 

furnish     a     bright    twi-  FIG.  28.-Twilight  phenomena. 

light.  When,  by  the  earth's  rotation,  this  observer  has  been 
carried  to  #,  all  the  region  to  the  east  of  his  zenith  lies  in 
the  shadow,  while  to  the  west  there  is  a  part  of  the  atmos- 
phere from  which  there  still  comes  a  twilight,  but  now  com- 
paratively faint,  because  the  lower  part  of  the  atmosphere 
about  our  observer  lies  in  the  shadow,  and  it  is  mainly 
its  upper  regions  from  which  the  light  comes,  and  here  the 
dust  and  moisture  are  much  less  abundant  than  in  the  lower 
strata.  Still  later,  when  the  observer  has  been  carried  by  the 
earth's  rotation  to  the  point  3,  every  vestige  of  twilight  will 
have  vanished  from  his  sky,  because  all  of  the  illuminated 
part  of  the  atmosphere  is  now  below  his  horizon,  which  is 
represented  by  the  line  8  L.  In  the  figure  the  sun  is  rep- 
resented to  be  78°  below  this  horizon  line  at  the  end  of  twi- 
light, but  this  is  a  gross  exaggeration,  made  for  the  sake  of 
clearness  in  the  drawing — in  fact,  twilight  is  usually  said 
to  end  when  the  sun  is  18°  below  the  horizon. 


84  ASTRONOMY 

Let  the  student  redraw  Fig.  28  on  a  large  scale,  so  that 
the  points  1  and  2  shall  be  only  18°  apart,  as  seen  from  the 
earth's  center.  He  will  find  that  the  point  L  is  brought 
down  much  closer  to  the  surface  of  the  earth,  and  measur- 
ing the  length  of  the  line  2  L,  he  should  find  for  the  "  height 
of  the  atmosphere  "  about  one-eightieth  part  of  the  radius 
of  the  earth — i.  e.,  a  little  less  than  50  miles.  This,  how- 
ever, is  not  the  true  height  of  the  atmosphere.  The  air 
extends  far  beyond  this,  but  the  particles  of  dust  and  vapor 
which  are  capable  of  sending  sunlight  down  to  the  earth 
seem  all  to  lie  below  this  limit. 

The  student  should  not  fail  to  watch  the  eastern  sky 
after  sunset,  and  see  the  shadow  of  the  earth  rise  up  and 
fill  it  while  the  twilight  arch  retreats  steadily  toward  the 
west. 

Duration  of  tivilight. — Since  twilight  ends  when  the  sun 
is  18°  below  the  horizon,  any  circumstance  which  makes 


FIG.  29.— The  cause  of  long  and  short  twilights. 

the  sun  go  down  rapidly  will  shorten  the  duration  of  twi- 
light, and  anything  which  retards  the  downward  motion 
of  the  sun  will  correspondingly  prolong  it.  Chief  among 
influences  of  this  kind  is  the  angle  which  the  sun's  course 
makes  with  the  horizon.  If  it  goes  straight  down,  as  at 
a,  Fig.  29,  a  much  shorter  time  will  suffice  to  carry  it  to 
a  depression  of  18°  than  is  needed  in  the  case  shown  at 
I  in  the  same  figure,  where  the  motion  is  very  oblique  to 
the  horizon.  If  we  consider  different  latitudes  and  differ- 
ent seasons  of  the  year,  we  shall  find  every  possible  variety 


THE  EARTH  AS  A  PLANET  85 

of  circumstance  from  a  to  #,  and  corresponding  to  these, 
the  duration  of  twilight  varies  from  an  all-night  duration 
in  the  summers  of  Scotland  and  more  northern  lands  to  a 
half  hour  or  less  in  the  mountains  of  Peru. 

Coleridge  does  not  much  exaggerate  the  shortness  of 
tropical  twilight  in  the  lines, 

"  The  sun's  rim  dips ;  the  stars  rush  out : 
At  one  stride  comes  the  dark." 

The,  Ancient  Mariner. 

In  the  United  States  the  longest  twilights  come  at  the 
end  of  June,  and  last  for  a  little  more  than  two  hours, 
while  the  shortest  ones  are  in  March  and  September, 
amounting  to  a  little  more  than  an  hour  and  a  half ;  but 
at  all  times  the  last  half  hour  of  twilight  is  hardly  to  be 
distinguished  from  night,  so  small  is  the  quantity  of  re- 
flecting matter  in  the  upper  regions  of  the  atmosphere. 
For  practical  convenience  it  is  customary  to  assume  in 
the  courts  of  law  that  twilight  ends  an  hour  after  sunset. 

How  long  does  twilight  last  at  the  north  pole  ? 

The  Aurora. — One  other  phenomenon  of  the  atmos- 
phere may  be  mentioned,  only  to  point  out  that  it  is  not 
of  an  astronomical  character.  The  Aurora,  or  northern 
lights,  is  as  purely  an  affair  of  the  earth  as  is  a  thunder- 
storm, and  its  explanation  belongs  to  the  subject  of  ter- 
restrial magnetism. 


CHAPTER  VI 

THE   MEASUREMENT   OP   TIME 

52.  Solar  time. — To  measure  any  quantity  we  need  a  unit 
in  terms  of  which  it  must  be  expressed.  Angles  are  meas- 
ured in  degrees,  and  the  degree  is  the  unit  for  angular  meas- 
urement. For  most  scientific  purposes  the  centimeter  is 
adopted  as  the  unit  with  which  to  measure  distances,  and 
similarly  a  day  is  the  fundamental  unit  for  the  measure- 
ment of  time.  Hours,  minutes,  and  seconds  are  aliquot 
parts  of  this  unit  convenient  for  use  in  dealing  with  shorter 
periods  than  a  day,  and  the  week,  month,  and  year  which 
we  use  in  our  calendars  are  multiples  of  the  day. 

Strictly  speaking,  a  day  is  not  the  time  required  by  the 
earth  to  make  one  revolution  upon  its  axis,  but  it  is  best 
defined  as  the  amount  of  time  required  for  a  particular  part 
of  the  sky  to  make  the  complete  circuit  from  the  meridian 
of  a  particular  place  through  west  and  east  back  to  the 
meridian  again.  The  day  begins  at  the  moment  when  this 
specified  part  of  the  sky  is  on  the  meridian,  and  "  the  time  " 
at  any  moment  is  the  hour  angle  of  this  particular  part  of 
the  sky — i.  e.,  the  number  of  hours,  minutes,  etc.,  tha£  have 
elapsed  since  it  was  on  the  meridian. 

The  student  has  already  become  familiar  with  the  kind 
of  day  which  is  based  upon  the  motion  of  the  vernal  equi- 
nox, and  which  furnishes  sidereal  time,  and  he  has  seen 
that  sidereal  time,  while  very  convenient  in  dealing  with 
the  motions  of  the  stars,  is  decidedly  inconvenient  for  the 
ordinary  affairs  of  life  since  in  the  reckoning  of  the  hours 
it  takes  no  account  of  daylight  and  darkness.  One  can  not 


THE  MEASUREMENT  OF  TIME  §7 

tell  off-hand  whether  10  hours,  sidereal  time,  falls  in  the  day 
or  in  the  night.  We  must  in  some  way  obtain  a  day  and  a 
system  of  time  reckoning  based  upon  the  apparent  diurnal 
motion  of  the  sun,  and  we  may,  if  we  choose,  take  the  sun 
itself  as  the  point  in  the  heavens  whose  transit  over  the 
meridian  shall  mark  the  beginning  and  the  end  of  the  day. 
In  this  system  "  the  time  "  is  the  number  of  hours,  minutes, 
etc.,  which  have  elapsed  since  the  sun  was  on  the  meridian, 
and  this  is  the  kind  of  time  which  is  shown  by  a  sun  dial, 
and  which  was  in  general  use,  years  ago,  before  clocks  and 
watches  became  common.  Since  the  sun  moves  among  the 
stars  about  a  degree  per  day,  it  is  easily  seen  that  the  rotat- 
ing earth  will  have  to  turn  farther  in  order  to  carry  any 
particular  meridian  from  the  sun  around  to  the  sun  again, 
than  to  carry  it  from  a  star  around  to  the  same  star,  or 
from  the  vernal  equinox  around  to  the  vernal  equinox 
again;  just  as  the  minute  hand  of  a  clock  turns  farther 
in  going  from  the  hour  hand  round  to  the  hour  hand  again 
than  it  turns  in  going  from  XII  to  XII.  These  solar  days 
and  hours  and  minutes  are  therefore  a  little  longer  than 
the  corresponding  sidereal  ones,  and  this  furnishes  the  ex- 
planation why  the  stars  come  to  the  meridian  a  little  ear- 
lier, by  solar  time,  every  night  than  on  the  night  before,  and 
why  sidereal  time  gains  steadily  upon  solar  time,  this  gain 
amounting  to  approximately  3m.  56.5s.  per  day,  or  exactly 
one  day  per  year,  since  the  sun  makes  the  complete  circuit 
of  the  constellations  once  in  a  year. 

With  the  general  introduction  of  clocks  and  watches 
into  use  about  a  century  ago  this  kind  of  solar  time  went 
out  of  common  use,  since  no  well-regulated  clock  could 
keep  the  time  correctly.  The  earth  in  its  orbital  motion 
around  the  sun  goes  faster  in  some  parts  of  its  orbit  than 
in  others,  and  in  consequence  the  sun  appears  to  move 
more  rapidly  among  the  stars  in  winter  than  in  summer ; 
moreover,  on  account  of  the  convergence  of  hour  circles 
as  we  go  away  from  the  equator,  the  same  amount  of  mo- 


88  ASTRONOMY 

tion  along  the  ecliptic  produces  more  effect  in  winter  and 
summer  when  the  sun  is  north  or  south,  than  it  does  in  the 
spring  and  autumn  when  the  sun  is  near  the  equator,  and 
as  a  combined  result  of  these  causes  and  other  minor  ones 
true  solar  time,  as  it  is  called,  is  itself  not  uniform,  but 
falls  behind  the  uniform  lapse  of  sidereal  time  at  a  variable 
rate,  sometimes  quicker,  sometimes  slower.  A  true  solar 
day,  from  noon  to  noon,  is  51  seconds  linger  in  September 
than  in  December. 

53.  Mean  solar  time. — To  remedy  these  inconveniences 
there   has  been  invented  and  brought  into  common  use 


+/5JW 

+fOm 

Om 
—5m 
—10m. 

z 

^-^ 

\ 

/ 
/ 
I 

\ 

/  

/ 

I 

> 

\ 

/ 

' 

\ 

f 

\ 

*  X 

/ 

' 

\ 

I 

— 

\ 

/ 

1 

\ 

/ 

Ja 

i 
n.f   Fcb.i  Ma 

r.t  Apr.fMa 

V  1  Jin 

e  1  Jv 

y  1  Ji, 

g.ffept.f    Oc 

t.1   Nor.f    DC 

c.i  Jaw./ 

FIG.  30.—  The  equation  of  time. 

what  is  called  mean  solar  time,  which  is  perfectly  uniform 
in  its  lapse  and  which,  by  comparison  with  sidereal  time, 
loses  exactly  one  day  per  year.  "  The  time  "  in  this  system 
never  differs  much  from  true  solar  time,  and  the  difference 
between  the  two  for  any  particular  day  may  be  found  in 
any  good  almanac,  or  may  be  read  from  the  curve  in  Fig. 
30,  in  which  the  part  of  the  curve  above  the  line  marked 
Om  shows  how  many  minutes  mean  solar  time  is  faster  than 
true  solar  time.  The  correct  name  for  this  difference  be- 
tween the  two  kinds  of  solar  time  is  the  equation  of  time,  but 
in  the  almanacs  it  is  frequently  marked  "  sun  fast  "  or  "  sun 
slow."  In  sidereal  time  and  true  solar  time  the  distinction 


THE  MEASUREMENT   OF  TIME  89 

between  A.  M.  hours  (ante  meridiem  =  before  the  sun  reaches 
the  meridian)  and  p.  M.  hours  (post  meridiem  =  after  the 
sun  has  passed  the  meridian)  is  not  observed,  "  the  time  " 
being  counted  from  0  hours  to  24  hours,  commencing  when 
the  sun  or  vernal  equinox  is  on  the  meridian.  Occasion- 
ally the  attempt  is  made  to  introduce  into  common  use 
this  mode  of  reckoning  the  hours,  beginning  the  day 
(date)  at  midnight  and  counting  the  hours  consecutively 
up  to  24,  when  the  next  date  is  reached  and  a  new  start 
made.  Such  a  system  would  simplify  railway  time  tables 
and  similar  publications  ;  but  the  American  public  is  slow 
to  adopt  it,  although  the  system  has  come  into  practical 
use  in  Canada  and  Spain. 

54.  To  find  (approximately)  the  sidereal  time  at  any  mo- 
ment. —  RULE  I.  When  the  mean  solar  time  is  known.  Let 
W  represent  the  time  shown  by  an  ordinary  watch,  and 
represent  by  S  the  corresponding  sidereal  time  and  by  D 
the  number  of  days  that  have  elapsed  from  March  23d  to 
the  date  in  question.  Then 

S=  W+ftxDX*. 

The  last  term  is  expressed  in  minutes,  and  should  be  re- 
duced to  hours  and  minutes.  Thus  at  4  p.  M.  on  July  4th  — 

D  =  103  days. 
f  J  X  D  X  4  =  406m. 

=  6h.  46m. 
W=4h.  Om. 

46m. 


The  daily  gain  of  sidereal  upon  mean  solar  time  is  f§-  of  4 
minutes,  and  March  23d  is  the  date  on  which  sidereal  and 
mean  solar  time  are  together,  taking  the  average  of  one  year 
with  another,  but  it  varies  a  little  from  year  to  year  on 
account  of  the  extra  day  introduced  in  leap  years. 

RULE  II.  When  the  stars  in  the  northern  sky  can  be 
seen.     Find  (3  Cassiopeiae,  and  imagine  a  line  drawn  from  it 
7 


90  ASTRONOMY 

to  Polaris,  and  another  line  from  Polaris  to  the  zenith. 
The  sidereal  time  is  equal  to  the  angle  between  these  lines, 
provided  that  that  angle  must  be  measured  from  the  zenith 
toward  the  west  Turn  the  angle  from  degrees  into  hours 
by  dividing  by  15. 

55.  The  earth's  rotation. — We  are  familiar  with  the  fact 
that  a  watch  may  run  faster  at  one  time  than  at  another, 
and  it  is  worth  while  to  inquire  if  the  same  is  not  true  of 
our  chief  timepiece — the  earth.     It  is  assumed  in  the  sec- 
tions upon  the  measurement  of  time  that  the  earth  turns 
about  its  axis  with  absolute  uniformity,  so  that  mean  solar 
time  never  gains  or  loses  even  the  smallest  fraction  of  a 
second.     Whether  this  be  absolutely  true  or  not,  no  one  has 
ever  succeeded  in  finding  convincing  proof  of  a  variation 
large  enough  to  be  measured,  although  it  has  recently  been 
shown  that  the  axis  about  which  it  rotates  is  not  perfectly 
fixed  within  the  body  of  the  earth.     The  solid  body  of  the 
earth  wriggles  about  this  axis  like  a  fish  upon  a  hook,  so 
that  the  position  of  the  north  pole  upon  the  earth's  sur- 
face changes  within  a  year  to  the  extent  of  40  or  50  feet 
(15  meters)  without  ever  getting  more  than  this  distance 
away  from  its  average  position.     This  is  probably  caused 
by  the  periodical  shifting  of  masses  of  air  and  water  from 
one  part  of  the  earth  to  another  as  the  seasons  change, 
and   it  seems  probable   that  these   changes  will   produce 
some  small  effect  upon  the  rotation  of  the  earth.     But  in 
spite  of  these,  for  any  such  moderate  interval  of  time  as  a 
year  or  a  century,  so  far  as  present  knowledge  goes,  we  may 
regard  the   earth's   rotation  as  uniform  and   undisturbed. 
For  longer  intervals— e.  g.,  1,000,000  or  10,000,000  years— 
the  question  is  a  very  different  one,  and  we  shall  have  to 
meet  it  again  in  another  connection. 

56.  Longitude  and  time.— In  what  precedes  there  has 
been  constant  reference  to  the  meridian.     The  day  begins 
when  the  sun  is  on  the  meridian.     Solar  time  is  the  angu- 
lar distance  of  the  sun  past  the  meridian.     Sidereal  time 


THE  MEASUREMENT  OF   TIME 


91 


FIG.  31. — Longitude  and  time. 


was  determined  by  observing  transits  of  stars  over  a  me- 
ridian line  actually  laid  out  upon  the  ground,  etc.  But 
every  place  upon  the  earth  has  its  own  meridian  from 
which  "  the  time  "  may  be  reckoned,  and  in  Fig.  31,  where 
the  rays  of  sunlight 
are  represented  as 
falling  upon  a  part 
of  the  earth's  equa- 
tor through  which 
the  meridians  o1 
New  York,  Chicago, 
and  San  Francisco 
pass,  it  is  evident 
that  these  rays  make 
different  angles  with 
the  meridians,  and 
that  the  sun  is  farther  from  the  meridian  of  New  York; 
than  from  that  of  San  Francisco  by  an  amount  just  equal 
to  the  angle  at  0  between  these  meridians.  This  angle  is 
called  by  geographers  the  difference  of  longitude  between 
the  two  places,  and  the  student  should  note  that  the  word 
longitude  is  here  used  in  a  different  sense  from  that  on 
page  36.  From  Fig.  31  we  obtain  the 

Theorem. — The  difference  between  "  the  times  "  at  any 
two  meridians  is  equal  to  their  difference  of  longitude,  and 
the  time  at  the  eastern  meridian  is  greater  than  at  the 
western  meridian.  Astronomers  usually  express  differences 
of  longitude  in  hours  instead  of  degrees.  Ih.  =  15°. 

The  name  given  to  any  kind  of  time  should  distinguish 
all  the  elements  which  enter  into  it — e.  g.,  New  York 
sidereal  time  means  the  hour  angle  of  the  vernal  equinox 
measured  from  the  meridian  of  New  York,  Chicago  true 
solar  time  is  the  hour  angle  of  the  sun  reckoned  from  the 
meridian  of  Chicago,  etc. 

57.  Standard  time. — The  requirements  of  railroad  traffic 
have  led  to  the  use  throughout  the  United  States  and 


THE   MEASUREMENT  OF   TIME  93 

Canada  of  four  "  standard  times,"  each  of  which  is  a  mean 
solar  time  some  integral  number  of  hours  slower  than  the 
time  of  the  meridian  passing  through  the  Royal  Observa- 
tory at  Greenwich,  England. 

Eastern  time  is  5  hours  slower  than  that  of  Greenwich. 
Central       "       6      " 
Mountain  "       7      " 
Pacific        "       8      " 

In  Fig.  32  the  broken  lines  indicate  roughly  the  parts  of 
the  United  States  and  Canada  in  which  these  several  kinds 
of  time  are  used,  and  illustrate  how  irregular  are  the  bound- 
aries of  these  parts. 

Standard  time  is  sent  daily  into  all  of  the  more  impor- 
tant telegraph  offices  of  the  United  States,  and  serves  to 
regulate  watches  and  clocks,  to  the  almost  complete  exclu- 
sion of  local  time. 

58.  To  determine  the  longitude. — With  an  ordinary  watch 
observe  the  time  of  the  sun's  transit  over  your  local  me- 
ridian, and  correct  the  observed  time  for  the  equation  of 
time  by  means  of  the  curve  in  Fig.  30.     The  difference 
between  the  corrected  time  and  12  o'clock  will  be  the  cor- 
rection of  your  watch  referred  to  local  mean  solar  time. 
Compare  your  watch  with  the  time  signals  in  the  nearest 
telegraph  office  and  find  its  correction  referred  to  standard 
time.     The  difference  between  the  two  corrections  is  the 
difference  between  your  longitude  and  that  of  the  standard 
meridian. 

X.  B. — Don't  tamper  with  the  watch  by  trying  to  "  set  it 
right."  No  harm  will  be  done  if  it  is  wrong,  provided  you 
take  due  account  of  the  correction  as  indicated  above. 

If  the  correction  of  the  watch  changed  between  your 
observation  and  the  comparison  in  the  telegraph  office, 
what  effect  would  it  have  upon  the  longitude  determina- 
tion ?  How  can  you  avoid  this  effect  ? 

59.  Chronology, — The  Century  Dictionary  defines  chro- 
nology as  "  the  science  of  time  " — that  is,  "  the  method  of 


94:  ASTRONOMY 

measuring  or  computing  time  by  regular  divisions  or  pe- 
riods according  to  the  revolutions  of  the  sun  or  moon." 

We  have  already  seen  that  for  the  measurement  of  short 
intervals  of  time  the  day  and  its  subdivisions — hours, 
minutes,  seconds — furnish  a  very  complete  and  convenient 
system.  But  for  longer  periods,  extending  to  hundreds  and 
thousands  of  days,  a  larger  unit  of  time  is  required,  and  for 
the  most  part  these  longer  units  have  in  all  ages  and  among 
all  peoples  been  based  upon  astronomical  considerations. 
But  to  this  there  is  one  marked  exception.  The  week  is  a 
simple  multiple  of  the  day,  as  the  dime  is  a  multiple  of  the 
cent,  and  while  it  may  have  had  its  origin  in  the  changing 
phases  of  the  moon  this  is  at  best  doubtful,  since  it  does 
not  follow  these  with  any  considerable  accuracy.  If  the 
still  longer  units  of  time— the  month  and  the  year — had 
equally  been  made  to  consist  of  an  integral  number  of  days 
much  confusion  and  misunderstanding  might  have  been 
avoided,  and  the  annals  of  ancient  times  would  have  pre- 
sented fewer  pitfalls  to  the  historian  than  is  now  the  case. 
The  month  is  plainly  connected  with  the  motion  of  the 
moon  among  the  stars.  The  year  is,  of  course,  based  upon 
the  motion  of  the  sun  through  the  heavens  and  the  change 
of  seasons  which  is  thus  produced ;  although,  as  commonly 
employed,  it  is  not  quite  the  same  as  the  time  required  by 
the  earth  to  make  one  complete  revolution  in  its  orbit. 
This  time  of  one  revolution  is  called  a  sidereal  year,  while, 
as  we  have  already  seen  in  Chapter  V,  the  year  which 
measures  the  course  of  the  seasons  is  shorter  than  this  on 
account  of  the  precession  of  the  equinoxes.  It  is  called  a 
tropical  year  with  reference  to  the  circuit  which  the  sun 
makes  from  one  tropic  to  the  other  and  back  again. 

We  can  readily  understand  why  primitive  peoples  should 
adopt  as  units  of  time  these  natural  periods,  but  in  so 
doing  they  incurred  much  the  same  kind  of  difficulty  that 
we  should  experience  in  trying  to  use  both  English  and 
American  money  in  the  ordinary  transactions  of  life.  How 


THE  MEASUREMENT  OF   TIME  95 

many  dollars  make  a  pound  sterling  ?  How  shall  we  make 
change  with  English  shillings  and  American  dimes,  etc.  ? 
How  much  is  one  unit  worth  in  terms  of  the  other  ? 

One  of  the  Greek  poets  *  has  left  us  a  quaint  account  of 
the  confusion  which  existed  in  his  time  with  regard  to  the* 
place  of  months  and  moons  in  the  calendar : 

"  The  moon  by  us  to  you  her  greeting  sends, 
But  bids  us  say  that  she's  an  ill-used  moon 
And  takes  it  much  amiss  that  you  will  still 
Shuffle  her  days  and  turn  them  topsy-turvy, 
So  that  when  gods,  who  know  their  feast  days  well, 
By  your  false  count  are  sent  home  supperless, 
They  scold  and  storm  at  her  for  your  neglect." 

60.  Day,  month,  and  year. — If  the  day,  the  month,  and 
the  year  are  to  be  used  concurrently,  it  is  necessary  to 
determine  how  many  days  are  contained  in  the  month  and 
year,  and  when  this  has  been  done  by  the  astronomer  the 
numbers  are  found  to  be  very  awkward  and  inconvenient 
for  daily  use ;  and  much  of  the  history  of  chronology 
consists  in  an  account  of  the  various  devices  by  which  in- 
genious men  have  sought  to  use  integral  numbers  to  replace 
the  cumbrous  decimal  fractions  which  follow. 

According  to  Professor  Harkness,  for  the  epoch  1900 
A.  D. — 

One  tropical  year  =  365.242197  mean  solar  days. 

"     =  365d.  5h.  48m.  45.8s. 
One  lunation         =  29.530588  mean  solar  days. 
=  29d.  12h.  44m.  2.8s. 

The  word  lunation  means  the  average  interval  from  one 
new  moon  to  the  next  one — i.  e.,  the  time  required  by  the 
moon  to  go  from  conjunction  with  the  sun  round  to  con- 
junction again. 

A  very  ancient  device  was  to  call  a  year  equal  to  365 

*  Aristophanes,  The  Clouds,  WhewelPs  translation. 


96  ASTRONOMY 

days,  and  to  have  months  alternately  of  29  and  30  days  in 
length,  but  this  was  unsatisfactory  in  more  than,  one  way. 
At  the  end  of  four  years  this  artificial  calendar  would  be 
about  one  day  ahead  of  the  true  one,  at  the  end  of  forty 
years  ten  days  in  error,  and  within  a  single  lifetime  the 
seasons  would  have  appreciably  changed  their  position  in 
the  year,  April  weather  being  due  in  March,  according  to 
the  calendar.  So,  too,  the  year  under  this  arrangement 
did  not  consist  of  any  integral  number  of  months,  12 
months  of  the  average  length  of  29.5  days  being  354  days, 
and  13  months  383.5  days,  thus  making  any  particular 
month  change  its  position  from  the  beginning  to  the  mid- 
dle and  the  end  of  the  year  within  a  comparatively  short 
time.  Some  peoples  gave  up  the  astronomical  year  as  an 
independent  unit  and  adopted  a  conventional  year  of  12 
lunar  months,  354  days,  which  is  now  in  use  in  certain 
Mohammedan  countries,  where  it  is  known  as  the  wander- 
ing year,  with  reference  to  the  changing  positions  of  the 
seasons  in  such  a  year.  Others  held  to  the  astronomical 
year  and  adopted  a  system  of  conventional  months,  such 
that  twelve  of  them  would  just  make  up  a  year,  as  is  done 
to  this  day  in  our  own  calendar,  whose  months  of  arbitrary 
length  we  are  compelled  to  remember  by  some  such  jingle 
as  the  following : 

"  Thirty  days  hath  September, 
April,  June,  and  November ; 
All  the  rest  have  thirty-one 
Save  February, 

Which  alone  hath  twenty-eight, 
Till  leap  year  gives  it  twenty-nine." 

61.  The  calendar. — The  foundations  of  our  calendar  may 
fairly  be  ascribed  to  Julius  Caesar,  who,  under  the  advice 
of  the  Egyptian  astronomer  Sosigines,  adopted  the  old 
Egyptian  device  of  a  leap  year,  whereby  every  fourth  year 
was  to  consist  of  366  days,  while  ordinary  years  were  only 
365  days  long.  He  also  placed  the  beginning  of  the  year 


THE   MEASUREMENT   OF   TIME  97 

at  the  first  of  January,  instead  of  in  March,  where  it  had 
formerly  been,  and  gave  his  own  name,  Julius,  to  the  month 
which  we  now  call  July.  August  was  afterward  named  in 
honor  of  his  successor^  Augustus.  The  names  of  the  earlier 
months  of  the  year  are  drawn  from  Eoman  mythology; 
those  of  the  later  months,  September,  October,  etc.,  mean- 
ing seventh  month,  eighth  month,  represent  the  places  of 
these  months  in  the  year,  before  Caesar's  reformation,  and 
also  their  places  in  some  of  the  subsequent  calendars,  for 
the  widest  diversity  of  practice  existed  during  mediaeval 
times  with  regard  to  the  day  on  which  -the  new  year  should 
begin,  Christmas,  Easter,  March  25th,  and  others  having  been 
employed  at  different  times  and  places. 

The  system  of  leap  years  introduced  by  Caesar  makes 
the  average  length  of  a  year  365.25  days,  which  differs  by 
about  eleven  minutes  from  the  true  length  of  the  tropical 
year,  a  difference  so  small  that  for  ordinary  purposes  no 
better  approximation  to  the  true  length  of  the  year  need 
be  desired.  But  any  deviation  from  the  true  length,  how- 
ever small,  must  in  the  course  of  time  shift  the  seasons,  the 
vernal  and  autumnal  equinox,  to  another  part  of  the  year, 
and  the  ecclesiastical  authorities  of  mediaeval  Europe  found 
here  ground  for  objection  to  Caesar's  calendar,  since  the 
great  Church  festival  of  Easter  has  its  date  determined 
with  reference  to  the  vernal  equinox,  and  with  the  lapse  of 
centuries  Easter  became  more  and  more  displaced  in  the 
calendar,  until  Pope  Gregory  XIII,  late  in  the  sixteenth 
century,  decreed  another  reformation,  whereby  ten  days 
were  dropped  from  the  calendar,  the  day  after  March  llth 
being  called  March  21st,  to  bring  back  the  vernal  equinox 
to  the  date  on  which  it  fell  in  A.  D.  325,  the  time  of  the 
Council  of  Nicaea,  which  Gregory  adopted  as  the  funda- 
mental epoch  of  his  calendar. 

The  calendar  having  thus  been  brought  back  into  agree- 
ment with  that  of  old  time,  Gregory  purposed  to  keep  it  in 
such  agreement  for  the  future  by  modifying  Caesar's  leap- 


98  ASTRONOMY 

year  rule  so  that  it  should  run  :  Every  year  whose  number 
is  divisible  by  4  shall  be  a  leap  year  except  those  years 
whose  numbers  are  divisible  by  100  but  not  divisible  by 
400.  These  latter  years — e.  g.,  1900 — are  counted  as  com- 
mon years.  The  calendar  thus  altered  is  called  Gregorian 
to  distinguish  it  from  the  older,  Julian  calendar,  and  it 
found  speedy  acceptance  in  those  civilized  countries  whose 
Church  adhered  to  Rome  ;  but  the  Protestant  powers  were 
slow  to  adopt  it,  and  it  was  introduced  into  England  and 
her  American  colonies  by  act  of  Parliament  in  the  year 
1752,  nearly  two  centuries  after  Gregory's  time.  In  Rus- 
sia the  Julian  calendar  has  remained  in  common  use  to 
our  own  day,  but  in  commercial  affairs  it  is  there  cus- 
tomary to  write  the  date  according  to  both  calendars — 
e.  g.,  July  T\,  and  at  the  present  time  strenuous  exertions 
are  making  in  that  country  for  the  adoption  of  the  Gre- 
gorian calendar  to  the  complete  exclusion  of  the  Julian 
one. 

The  Julian  and  Gregorian  calendars  are  frequently  rep- 
resented by  the  abbreviations  0.  S.  and  N".  S.,  old  style, 
new  style,  and  as  the  older  historical  dates  are  usually  ex- 
pressed in  0.  S.,  it  is  sometimes  convenient  to  transform  a 
date  from  the  one  calendar  to  the  other.  This  is  readily 
done  by  the  formula 

0  =  ./•+(.»•- 2) -J 

where  G  and  J  are  the  respective  dates,  N  is  the  number 
of  the  century,  and  the  remainder  is  to  be  neglected  in  the 
division  by  4.  For  September  3,  1752,  0.  S.,  we  have 

,7=  Sept.  3 

N-2  =   +15 


G  =  Sept.  14 


THE   MEASUREMENT  OF   TIME  99 

and  September  14  is  the  date  fixed  by  act  of  Parliament  to 
correspond  to  September  3,  1752,  0.  S.  Columbus  discovered 
America  on  October  12,  1492,  0.  S.  What  is  the  corre- 
sponding date  in  the  Gregorian  calendar  ? 

62.  The  day  of  the  week,  —  A  problem  similar  to  the 
above  but  more  complicated  consists  in  finding  the  day  of 
the  week  on  which  any  given  date  of  the  Gregorian  cal- 
endar falls—  e.  g.,  October  21,  1492. 

The  formula  for  this  case  is 

Y-l       Y-l       Y-l 


where  Y  denotes  the  given  year,  D  the  number  of  the  day 
(date)  in  that  year,  and  q  and  r  are  respectively  the  quo- 
tient and  the  remainder  obtained  by  dividing  the  second 
member  of  the  equation  by  7.  If  r  —  1  the  date  falls  on 
Sunday,  etc.,  and  if  r  =  0  the  day  is  Saturday.  For  the 
example  suggested  above  we  have 

Jan.    31  Y                  =  1492 

Feb.    29  -\-D                  —  +295 

Mch.  31  +(;r_i)_±-      4=  +  373 

April  30  -  (  r  -  1)  -^  100  =  14 

May    31  +  (Y  —  1)  -f-  400  =  +      3 

June  30  ~*j~^L48 

July   31 

Aug.  31  0=         306 

Sept.  30  r  =  6  =  Friday. 

Oct.    21 


Find  from  some  history  the  day  of  the  week  on  which 
Columbus  first  saw  America,  and  compare  this  with  the 
above. 

On  what  day  of  the  week  did  last  Christmas  fall  ?  On 
what  day  of  the  week  were  you  born  ?  In  the  formula  for 
the  day  of  the  week  why  does  q  have  the  coefficient  7  ? 


100  ASTRONOMY 

What  principles  in  the  calendar  give  rise  to  the  divisors  4, 
100,400? 

For  much  curious  and  interesting  information  about 
methods  of  reckoning  the  lapse  of  time  the  student  may 
consult  the  articles  Calendar  and  Chronology  in  any  good 
encyclopaedia. 


CHAPTEE  VII 

ECLIPSES 

63.  The  nature  of  eclipses. — Every  planet  has  a  shadow 
which  travels  with  the  planet  along  its  orbit,  always  point- 
ing directly  away  from  the  sun,  and  cutting  off  from  a  cer- 
tain region  of  space  the  sunlight  which  otherwise  would  fill 
it.  For  the  most  part  these  shadows  are  invisible,  but  occa- 
sionally one  of  them  falls  upon  a  planet  or  some  other  body 
which  shines  by  reflected  sunlight,  and,  cutting  off  its  sup- 
ply of  light,  produces  the  striking  phenomenon  which  we 
call  an  eclipse.  The  satellites  of  Jupiter,  Saturn,  and  Mars 
are  eclipsed  whenever  they  plunge  into  the  shadows  cast  by 
their  respective  planets,  and  Jupiter  himself  is  partially 
eclipsed  when  one  of  his  own  satellites  passes  between  him 
and  the  sun,  and  casts  upon  his  broad  surface  a  shadow  too 
small  to  cover  more  than  a  fraction  of  it. 

But  the  eclipses  of  most  interest  to  us  are  those  of  the 
sun  and  moon,  called  respectively  solar  and  lunar  eclipses. 
In  Fig.  33  the  full  moon,  M' ,  is  shown  immersed  in  the 
shadow  cast  by  the  earth,  and  therefore  eclipsed,  and  in  the 
same  figure  the  new  moon,  Jf,  is  shown  as  casting  its  shadow 
upon  the  earth  and  producing  an  eclipse  of  the  sun.  From 
a  mere  inspection  of  the  figure  we  may  learn  that  an  eclipse 
of  the  sun  can  occur  only  at  new  moon — i.  e.,  when  the 
moon  is  on  line  between  the  earth  and  sun — and  an  eclipse 
of  the  moon  can  occur  only  at  full  moon.  Why  ?  Also,  the 
eclipsed  moon,  M' ,  will  present  substantially  the  same  ap- 
pearance from  every  part  of  the  earth  where  it  is  at  all  vis- 
ible— the  same  from  North  America  as  from  South  Amer- 

101 


ASTRONOMY 

§,  ica — but  the  eclipsed  sun  will  present  very 
.different  aspects  from  different  parts  of 
the  earth.  Thus,  at  L,  within  the  moon's 
shadow,  the  sunlight  will  be  entirely  cut 
off,  producing  what  is  called  a  total  eclipse. 
At  points  of  the  earth's  surface  near  J  and 
K  there  will  be  no  interference  whatever 
with  the  sunlight,  and  no  eclipse,  since  the 
moon  is  quite  off  the  line  joining  these  re- 
gions to  any  part  of  the  sun.  At  places  be- 
tween J  and  L  or  K  and  L  the  moon  will 
cut  off  a  part  of  the  sun's  light,  but  not  all 
of  it,  and  will  produce  what  is  called  a  par- 
\  tial  eclipse,  which,  as  seen  from  the  north- 
i  ern  parts  of  the  earth,  will  be  an  eclipse  of 
the  lower  (southern)  part  of  the  sun,  and 
as  seen  from  the  southern  hemisphere  will 
be  an  eclipse  of  the  northern  part  of  the 


sun. 


The  moon  revolves  around  the  earth  in 
a  plane,  which,  in  the  figure,  we  suppose  to 
be  perpendicular  to  the  surface  of  the  pa- 
per, and  to  pass  through  the  sun  along  the 
line  M'  M  produced.  But  it  frequently 
happens  that  this  plane  is  turned  to  one 
side  of  the  sun,  along  some  such  line  as 
P  Q,  and  in  this  case  the  full  moon  would 
cut  through  the  edge  of  the  earth's  shadow 
without  being  at  any  time  wholly  immersed 
in  it,  giving  a  partial  eclipse  of  the  moon, 
as  is  shown  in  the  figure. 

In  what  parts  of  the  earth  would  this 
eclipse  be  visible?  What  kinds  of  solar 
eclipse  would  be  produced  by  the  new  moon 
at  Q?  In  what  parts  of  the  earth  would 
they  be  visible  ? 


ECLIPSES  103 

64.  The  shadow  cone. — The  shape  and  position  of  the 
earth's  shadow  are  indicated  in  Fig.  33  by  the  lines  drawn 
tangent  to  the  circles  which  represent  the  sun  and  earth, 
since  it  is  only  between  these  lines  that  the  earth  interferes 
with  the  free  radiation  of  sunlight,  and  since  both  sun  and 
earth  are  spheres,  and  the  earth  is  much  the  smaller  of  the 
two,  it  is  evident  that  the  earth's  shadow  must  be,  in  geo- 
metrical language,  a  cone  whose  base  is  at  the  earth,  and 
whose  vertex  lies  far  to  the  right  of  the  figure — in  other 
words,  the  earth's  shadow,  although  very  long,  tapers  off 
finally  to  a  point  and  ends.  So,  too,  the  shadow  of  the 
moon  is  a  cone,  having  its  base  at  the  moon  and  its  vertex 
turned  away  from  the  sun,  and,  as  shown  in  the  figure,  just 
about  long  enough  to  reach  the  earth. 

It  is  easily  shown,  by  the  theorem  of  similar  triangles  in 
connection  with  the  known  size  of  the  earth  and  sun,  that 
the  distance  from  the  center  of  the  earth  to  the  vertex  of 
its  shadow  is  always  equal  to  the  distance  of  the  earth  from 
the  sun  divided  by  108,  and,  similarly,  that  the  length  of 
the  moon's  shadow  is  equal  to  the  distance  of  the  moon 
from  the  sun  divided  by  400,  the  moon's  shadow  being  the 
smaller  and  shorter  of  the  two,  because  the  moon  is  smallei 
than  the  earth.  The  radius  of  the  moon's  orbit  is  just  about 
T£¥th  part  of  the  radius  of  the  earth's  orbit — i.  e.,  the  dis- 
tance of  the  moon  from  the  earth  is  ¥i^th  part  of  the  dis- 
tance of  the  earth  from  the  sun,  and  it  is  this  "  chance  " 
agreement  between  the  length  of  the  moon's  shadow  and 
the  distance  of  the  moon  from  the  earth  which  makes  the 
tip  of  the  moon's  shadow  fall  very  near  the  earth  at  the 
time  of  solar  eclipses.  Indeed,  the  elliptical  shape  of  the 
moon's  orbit  produces  considerable  variations  in  the  dis- 
tance of  the  moon  from  the  earth,  and  in  consequence  of 
these  variations  the  vertex  of  the  shadow  sometimes  falls 
short  of  reaching  the  earth,  and  sometimes  even  projects 
considerably  beyond  its  farther  side.  When  the  moon's 
distance  is  too  great  for  the  shadow  to  bridge  the  space  be- 


104  ASTRONOMY 

tween  earth  and  moon  there  can  be  no  total  eclipse  of  the 
sun,  for  there  is  no  shadow  which  can  fall  upon  the  earth, 
even  though  the  moon  does  come  directly  between  earth 
and  sun.  But  there  is  then  produced  a  peculiar  kind  of 
partial  eclipse  called  annular,  or  ring-shaped,  because  the 
moon,  although  eclipsing  the  central  parts  of  the  sun,  is 
not  large  enough  to  cover  the  whole  of  it,  but  leaves  the 
sun's  edge  visible  as  a  ring  of  light,  which  completely  sur- 
rounds the  moon.  Although,  strictly  speaking,  this  is  only 
a  partial  eclipse,  it  is  customary  to  put  total  and  annular 
eclipses  together  in  one  class,  which  is  called  central  eclipses, 
since  in  these  eclipses  the  line  of  centers  of  sun  and  moon 
strikes  the  earth,  while  in  ordinary  partial  eclipses  it  passes 
to  one  side  of  the  earth  without  striking  it.  In  this  latter 
case  we  have  to  consider  another  cone  called  the  penumbra 
— i.  e.,  partial  shadow — which  is  shown  in  Fig.  33  by  the 
broken  lines  tangent  to  the  sun  and  moon,  and  crossing  at 
the  point  F,  which  is  the  vertex  of  this  cone.  This  penum- 
bral  cone  includes  within  its  surface  all  that  region  of  space 
within  which  the  moon  cuts  off  any  of  the  sunlight,  and 
of  course  it  includes  the  shadow  cone  which  produces  total 
eclipses.  Wherever  the  penumbra  falls  there  will  be  a  solar 
eclipse  of  some  kind,  and  the  nearer  the  place  is  to  the  axis 
of  the  penumbra,  the  more  nearly  total  will  be  the  eclipse. 
Since  the  moon  stands  about  midway  between  the  earth  and 
the  vertex  of  the  penumbra,  the  diameter  of  the  penumbra 
where  it  strikes  the  earth  will  be  about  twice  as  great  as 
the  diameter  of  the  moon,  and  the  student  should  be  able 
to  show  from  this  that  the  region  of  the  earth's  surface 
within  which  a  partial  solar  eclipse  is  visible  extends  in  a 
straight  line  about  2,100  miles  on  either  side  of  the  region 
where  the  eclipse  is  total.  Measured  along  the  curved 
surface  of  the  earth,  this  distance  is  frequently  much 
greater. 

Is  it  true  that  if  at  any  time  the  axis  of  the  shadow  cone 
comes  within  2,100  miles  of  the  earth's  surface  a  partial 


ECLIPSES  105 

eclipse  will  be  visible  in  those  parts  of  the  earth  nearest  the 
axis  of  the  shadow  ? 

65.  Different  characteristics  of  lunar  and  solar  eclipses. — 
One  marked  difference  between  lunar  and  solar  eclipses 
which  has  been  already  suggested,  may  be  learned  from  Fig. 
33.  The  full  moon,  M' ,  will  be  seen  eclipsed  from  every 
part  of  the  earth  where  it  is  visible  at  all  at  the  time  of  the 
eclipse — that  is,  from  the  whole  night  side  of  the  earth ; 
while  the  eclipsed  sun  will  be  seen  eclipsed  only  from  those 
parts  of  the  day  side  of  the  earth  upon  which  the  moon's 
shadow  or  penumbra  falls.  Since  the  point  of  the  shadow 
at  best  but  little  more  than  reaches  to  the  earth,  the 
amount  of  space  upon  the  earth  which  it  can  cover  at  any 
one  moment  is  very  small,  seldom  more  than  100  to  200 
miles  in  length,  and  it  is  only  within  the  space  thus  ac- 
tually covered  by  the  shadow  that  the  sun  is  at  any  given 
moment  totally  eclipsed,  but  within  this  region  the  sun 
disappears,  absolutely,  behind  the  solid  body  of  the  moon, 
leaving  to  view  only  such  outlying  parts  and  appendages  as 
are  too  large  for  the  moon  to  cover.  At  a  lunar  eclipse,  on 
the  other  hand,  the  earth  coming  between  sun  and  moon 
cuts  off  the  light  from  the  latter,  but,  curiously  enough, 
does  not  cut  it  off  so  completely  that  the  moon  disappears 
altogether  from  sight  even  in  mid-eclipse.  The  explana- 
tion of  this  continued  visibility  is  furnished  by  the  broken 
lines  extending,  in  Fig.  33,  from  the  earth  through  the 
moon.  These  represent  sunlight,  which,  entering  the 
earth's  atmosphere  near  the  edge  of  the  earth  (edge  as  seen 
from  sun  and  moon),  passes  through  it  and  emerges  in  a 
changed  direction,  refracted,  into  the  shadow  cone  and 
feebly  illumines  the  moon's  surface  with  a  ruddy  light  like 
that  often  shown  in  our  red  sunsets.  Eclipse  and  sunset 
alike  show  that  when  the  sun's  light  shines  through  dense 
layers  of  air  it  is  the  red  rays  which  come  through  most 
freely,  and  the  attentive  observer  may  often  see  at  a  clear 
sunset  something  which  corresponds  exactly  to  the  bending 
8 


106  ASTRONOMY 

of  the  sunlight  into  the  shadow  cone ;  just  before  the  sun 
reaches  the  horizon  its  disk  is  distorted  from  a  circle  into 
an  oval  whose  horizontal  diameter  is  longer  than  the  verti- 
cal one  (see  §  49). 

QUERY. — At  a  total  lunar  eclipse  what  would  be  the 
effect  upon  the  appearance  of  the  moon  if  the  atmosphere 
around  the  edge  of  the  earth  were  heavily  laden  with 
clouds  ? 

66.  The  track  of  the  shadow. — We  may  regard  the  moon's 
shadow  cone  as  a  huge  pencil  attached  to  the  moon,  mov- 
ing with  it  along  its  orbit  in  the  direction  of  the  arrow- 
head (Fig.  34),  and  as  it  moves  drawing  a  black  line  across 
the  face  of  the  earth  at  the  time  of  total  eclipse.  This  black 
line  is  the  path  of  the  shadow  and  marks  out  those  regions 
within  which  the  eclipse  will  be  total  at  some  stage  of  its 
progress.  If  the  point  of  the  shadow  just  reaches  the 
earth  its  trace  will  have  no  sensible  width,  while,  if  the 
moon  is  nearer,  the  point  of  the  cone  will  be  broken  off, 
and,  like  a  blunt  pencil,  it  will  draw  a  broad  streak  across 
the  earth,  and  this  under  the  most  favorable  circumstances 
may  have  a  breadth  of  a  little  more  than  160  miles  and  a 
length  of  10,000  or  12,000  miles.  The  student  should 
be  able  to  show  from  the  known  distance  of  the  moon 
(240,000  miles)  and  the  known  interval  between  consecutive 
new  moons  (29.5  days)  that  on  the  average  the  moon's 
shadow  sweeps  past  the  earth  at  the  rate  of  2,100  miles  per 
hour,  and  that  in  a  general  way  this  motion  is  from  west 
to  east,  since  that  is  the  direction  of  the  moon's  motion  in 
its  orbit.  The  actual  velocity  with  which  the  moon's  shadow 
moves  past  a  given  station  may,  however,  be  considerably 
greater  or  less  than  this,  since  on  the  one  hand  when  the 
shadow  falls  very  obliquely,  as  when  the  eclipse  occurs  near 
sunrise  or  sunset,  the  shifting  of  the  shadow  will  be  very 
much  greater  than  the  actual  motion  of  the  moon  which 
produces  it,  and  on  the  other  hand  the  earth  in  revolving 
upon  its  axis  carries  the  spectator  and  the  ground  upon 


ECLIPSES  107 

which  he  stands  along  the  same  direction  in  which  the 
shadow  is  moving.  At  the  equator,  with  the  sun  and  moon 
overhead,  this  motion  of  the  earth  subtracts  about  1,000 
miles  per  hour  from  the  velocity  with  which  the  shadow 
passes  by.  It  is  chiefly  on  this  account,  the  diminished 
velocity  with  which  the  shadow  passes  by,  that  total  solar 
eclipses  last  longer  in  the  tropics  than  in  higher  latitudes, 
but  even  under  the  most  favorable  circumstances  the  dura- 
tion of  totality  does  not  reach  eight  minutes  at  any  one 
place,  although  it  may  take  the  shadow  several  hours  to 
sweep  the  entire  length  of  its  path  across  the  earth. 

According  to  Whitmell  the  greatest  possible  duration  of 
a  total  solar  eclipse  is  7m.  40s.,  and  it  can  attain  this  limit 
only  when  the  eclipse  occurs  near  the  beginning  of  July 
and  is  visible  at  a  place  5°  north  of  the  equator. 

The  duration  of  a  lunar  eclipse  depends  mainly  upon 
the  position  of  the  moon  with  respect  to  the  earth's  shadow. 
If  it  strikes  the  shadow  centrally,  as  at  Jf' ,  Fig.  33,  a  total 
eclipse  may  last  for  about  two  hours,  with  an  additional 
hour  at  the  beginning  and  end,  during  which  the  moon  is 
entering  and  leaving  the  earth's  shadow.  If  the  moon 
meets  the  shadow  at  one  side  of  the  axis,  as  at  P,  the  total 
phase  of  the  eclipse  may  fail  altogether,  and  between  these 
extremes  the  duration  of  totality  may  be  anything  from 
two  hours  downward. 

67.  Relation  of  the  lunar  nodes  to  eclipses. — To  show  why 
the  moon  sometimes  encounters  the  earth's  shadow  cen- 
trally and  more  frequently  at  full  moon  passes  by  without 
touching  it  at  all,  we  resort  to  Fig.  34,  which  represents  a 
part  of  the  orbit  of  the  earth  about  the  sun,  with  dates 
showing  the  time  in  each  year  at  which  the  earth  passes 
the  part  of  its  orbit  thus  marked.  The  orbit  of  the  moon 
about  the  earth,  M  M',  is  also  shown,  with  the  new  moon, 
Jf,  casting  its  shadow  toward  the  earth  and  the  full  moon, 
Jfaf',  apparently  immersed  in  the  earth's  shadow.  But  here 
appearances  are  deceptive,  and  the  student  who  has  made 


108  ASTRONOMY 

the  observations  set  forth  in  Chapter  III  has  learned  for 
himself  a  fact  of  which  careful  account  must  now  be  taken. 
The  apparent  paths  of  the  moon  and  sun  among  the  stars 
are  great  circles  which  lie  near  each  other,  but  are  not 
exactly  the  same ;  and  since  these  great  circles  are  only  the 
intersections  of  the  sky  with  the  planes  of  the  earth's  orbit 


FIG.  34.— Relation  of  the  lunar  nodes  to  eclipses. 

and  the  moon's  orbit,  we  see  that  these  planes  are  slightly 
inclined  to  each  other  and  must  therefore  intersect  along 
some  line  passing  through  the  center  of  the  earth.  This 
line,  N'  N" ',  is  shown  in  the  figure,  and  if  we  suppose  the 
surface  of  the  paper  to  represent  the  plane  of  the  earth's 
orbit,  we  shall  have  to  suppose  the  moon's  orbit  to  be  tipped 
around  this  line,  so  that  the  left  side  of  the  orbit  lies  above 
and  the  right  side  below  the  surface  of  the  paper.  But 
since  the  earth's  shadow  lies  in  the  plane  of  its  orbit — i.  e., 
in  the  surface  of  the  paper — the  full  moon  of  March,  Jf' , 
must  have  passed  below  the  shadow,  and  the  new  moon,  J/, 
must  have  cast  its  shadow  above  the  earth,  so  that  neither 
a  lunar  nor  a  solar  eclipse  could  occur  in  that  month.  But 
toward  the  end  of  May  the  earth  and  moon  have  reached 
a  position  where  the  line  N'  N"  points  almost  directly 
toward  the  sun,  in  line  with  the  shadow  cones  which  hide 
it.  Note  that  the  line  N'  N"  remains  very  nearly  parallel 
to  its  original  position,  while  the  earth  is  moving  along 


ECLIPSES  109 

its  orbit.  The  full  moon  will  now  be  very  near  this  line 
and  therefore  very  close  to  the  plane  of  the  earth's  orbit,  if 
not  actually  in  it,  and  must  pass  through  the  shadow  of  the 
earth  and  be  eclipsed.  So  also  the  new  moon  will  cast  its 
shadow  in  the  plane  of  the  ecliptic,  and  this  shadow,  falling 
upon  the  earth,  produced  the  total  solar  eclipse  of  May  28, ' 
1900. 

N1  N"  is  called  the  line  of  nodes  of  the  moon's  orbit  (§  39), 
and  the  two  positions  of  the  earth  in  its  orbit,  diametrically 
opposite  each  other,  at  which  N'  N"  points  exactly  toward 
the  sun,  we  shall  call  the  nodes  of  the  lunar  orbit.  Strictly 
speaking,  the  nodes  are  those  points  of  the  sky  against 
which  the  moon's  center  is  projected  at  the  moment  when 
in  its  orbital  motion  it  cuts  through  the  plane  of  the  earth's 
orbit.  Bearing  in  mind  these  definitions,  we  may  condense 
much  of  what  precedes  into  the  proposition :  Eclipses  of 
either  sun  or  moon  can  occur  only  when  the  earth  is  at  or 
near  one  of  the  nodes  of  the  moon's  orbit.  Corresponding 
to  these  positions  of  the  earth  there  are  in  each  year  two 
seasons,  about  six  months  apart,  at  which  times,  and  at 
these  only,  eclipses  can  occur.  Thus  in  the  year  1900  the 
earth  passed  these  two  points  on  June  2d  and  November 
24th  respectively,  and  the  following  list  of  eclipses  which 
occurred  in  that  year  shows  that  all  of  them  were  within  a 
few  days  of  one  or  the  other  of  these  dates : 

Eclipses  of  the  Year  1900 

Total  solar  eclipse May  28th. 

Partial  lunar  eclipse June  12th. 

Annular  (solar)  eclipse November  21st. 

68.  Eclipse  limits. — If  the  earth  is  exactly  at  the  node  at 
the  time  of  new  moon,  the  moon's  shadow  will  fall  cen- 
trally upon  it  and  will  produce  an  eclipse  visible  within  the 
torrid  zone,  since  this  is  that  part  of  the  earth's  surface 
nearest  the  plane  of  its  orbit.  If  the  earth  is  near  but  not 
at  the  node,  the  new  moon  will  stand  a  little  north  or  south 


110  ASTRONOMY 

of  the  plane  of  the  earth's  orbit,  and  its  shadow  will  strike 
the  earth  farther  north  or  south  than  before,  producing  an 
eclipse  in  the  temperate  or  frigid  zones ;  or  the  shadow  may 
even  pass  entirely  above  or  below  the  earth,  producing  no 
eclipse  whatever,  or  at  most  a  partial  eclipse  visible  near 
the  north  or  south  pole.  Just  how  many  days'  motion  the 
earth  may  be  away  from  the  node  and  still  permit  an  eclipse 
is  shown  in  the  following  brief  table  of  eclipse  limits,  as 
they  are  called  : 

Solar  Eclipse  Limits 
If  at  any  new  moon  the  earth  is 

Less  than  10  days  away  from  a  node,  a  central  eclipse  is  certain. 

Between  10  and  16  days    "     "     "      some  kind  of  eclipse  is  certain. 

Between  16  and  19  days     "     "     "      a  partial  eclipse  is  possible. 

More  than  19  days  "     "     "      no  eclipse  is  possible. 

Lunar  Eclipse  Limits 
If  at  any  full  moon  the  earth  is 

Less  than  4  days  away  from  a  node,  a  total  eclipse  is  certain. 
Between  4  and  10  days    "      "     "      some  kind  of  eclipse  is  certain. 
Between  10  and  14  days  "     "     "      a  partial  eclipse  is  possible. 
More  than  14  days  "     "     "       no  eclipse  is  possible. 

From  this  table  of  eclipse  limits  we  may  draw  some 
interesting  conclusions  about  the  frequency  with  which 
eclipses  occur. 

69.  Number  of  eclipses  in  a  year. — Whenever  the  earth 
passes  a  node  of  the  moon's  orbit  a  new  moon  must  occur  at 
some  time  during  the  2  X  16  days  that  the  earth  remains 
inside  the  limits  where  some  kind  of  eclipse  is  certain,  and 
there  must  therefore  be  an  eclipse  of  the  sun  every  time  the 
earth  passes  a  node  of  the  moon's  orbit.  But,  since  there 
are  two  nodes  past  which  the  earth  moves  at  least  once  in 
each  year,  there  must  be  at  least  two  solar  eclipses  every 
year.  Can  there  be  more  than  two  ?  On  the  average,  will 
central  or  partial  eclipses  be  the  more  numerous  ? 

A  similar  line  of  reasoning  will  not  hold  true  for 
eclipses  of  the  moon,  since  it  is  quite  possible  that  no  full 


ECLIPSES  HI 

moon  should  occur  during  the  20  days  required  by  the 
earth  to  move  past  the  node  from  the  western  to  the  east- 
ern limit.  This  omission  of  a  full  moon  while  the  earth  is 
within  the  eclipse  limits  sometimes  happens  at  both  nodes 
in  the  same  year,  and  then  we  have  a  year  with  no  eclipse 
of  the  moon.  The  student  may  note  in  the  list  of  eclipses 
for  1900  that  the  partial  lunar  eclipse  of  June  12th  oc- 
curred 10  days  after  the  earth  passed  the  node,  and  was 
therefore  within  the  doubtful  zone  where  eclipses  may 
occur  and  may  fail,  and  corresponding  to  this  position  the 
eclipse  was  a  very  small  one,  only  a  thousandth  part  of  the 
moon's  diameter  dipping  into  the  shadow  of  the  earth. 
By  so  much  the  year  1900  escaped  being  an  illustration  of 
a  year  in  which  no  lunar  eclipse  occurred. 

A  partial  eclipse  of  the  moon  will  usually  occur  about  a 
fortnight  before  or  after  a  total  eclipse  of  the  sun,  since 
the  full  moon  will  then  be  within  the  eclipse  limit  at  the 
opposite  node.  A  partial  eclipse  of  the  sun  will  always 
occur  about  a  fortnight  before  or  after  a  total  eclipse  of  the 
moon. 

70.  Eclipse  maps. — It  is  the  custom  of  astronomers  to 
prepare,  in  advance  of  the  more  important  eclipses,  maps 
showing  the  trace  of  the  moon's  shadow  across  the  earth, 
and  indicating  the  times  of  beginning  and  ending  of  the 
eclipses,  as  is  shown  in  Fig.  35.  While  the  actual  construc- 
tion of  such  a  map  requires  much  technical  knowledge,  the 
principles  involved  are  simple  enough :  the  straight  line 
passed  through  the  center  of  sun  and  moon  is  the  axis  of 
the  shadow  cone,  and  the  map  contains  little  more  than  a 
graphical  representation  of  when  and  where  this  cone  meets 
the  surface  of  the  earth.  Thus  in  the  map,  the  "  Path  of 
Total  Eclipse  "  is  the  trace  of  the  shadow  cone  across  the 
face  of  the  earth,  and  the  width  of  this  path  shows  that  the 
earth  encountered  the  shadow  considerably  inside  the  ver- 
tex of  the  cone.  The  general  direction  of  the  path  is  from 
west  to  east,  and  the  slight  sinuosities  which  it  presents 


ECLIPSES  113 

are  for  the  most  part  due  to  unavoidable  distortion  of  the 
map  caused  by  the  attempt  to  represent  the  curved  surface 
of  the  earth  upon  the  flat  surface  of  the  paper.  On  either 
side  of  the  Path  of  Total  Eclipse  is  the  region  within  which 
the  eclipse  was  only  partial,  and  the  broken  lines  marked  Be- 
gins at  3h.,  Ends  at  3h.,  show  the  intersection  of  the  penum- 
bral  cone  with  the  surface  of  the  earth  at  3  P.  M.,  Green*- 
wich  time.  These  two  lines  inclose  every  part  of  the  earth's 
surface  from  which  at  that  time  any  eclipse  whatever  could 
be  seen,  and  at  this  moment  the  partial  eclipse  was  just  be- 
ginning at  every  point  on  the  eastern  edge  of  the  penumbra 
and  just  ending  at  every  point  on  the  western  edge,  while 
at  the  center  of  the  penumbra,  on  the  Path  of  Total  Eclipse, 
lay  the  shadow  of  the  moon,  an  oval  patch  whose  greatest 
diameter  was  but  little  more  than  60  miles  in  length,  and 
within  which  lay  every  part  of  the  earth  where  the  eclipse 
was  total  at  that  moment. 

The  position  of  the  penumbra  at  other  hours  is  also 
shown  on  the  map,  although  with  more  distortion,  because 
it  then  meets  the  surface  of  the  earth  more  obliquely,  and 
from  these  lines  it  is  easy  to  obtain  the  time  of  beginning 
and  end  of  the  eclipse  at  any  desired  place,  and  to  estimate 
by  the  distance  of  the  place  from  the  Path  of  Total  Eclipse 
how  much  of  the  sun's  face  was  obscured. 

Let  the  student  make  these  "  predictions  "  for  Washing- 
ton, Chicago,  London,  and  Algiers. 

The  points  in  the  map  marked  First  Contact,  Last  Con- 
tact, show  the  places  at  which  the  penumbral  cone  first 
touched  the  earth  and  finally  left  it.  According  to  compu- 
tations made  as  a  basis  for  the  construction  of  the  map  the 
Greenwich  time  of  First  Contact  was  Oh.  12.5m.  and  of  Last 
Contact  5h.  35.6m.,  and  the  difference  between  these  two 
times  gives  the  total  duration  of  the  eclipse  upon  the  earth 
— i.  e.,  5  hours  23.1  minutes. 

71.  Future  eclipses. — An  eclipse  map  of  a  different  kind 
is  shown  in  Fig.  36,  which  represents  the  shadow  paths  of 


114 


ASTRONOMY 


all  the  central  eclipses  of  the  sun,  visible  during  the  period 
1900-1918  A.  D.,  in  those  parts  of  the  earth  north  of  the 
south  temperate  zone.  Each  continuous  black  line  shows 
the  path  of  the  shadow  in  a  total  eclipse,  from  its  begin- 


FIG.  36.— Central  eclipses  for  the  first  two  decades  of  the  twentieth  century. 
OPPOLZEB. 

ning,  at  sunrise,  at  the  western  end  of  the  line  to  its  end, 
sunset,  at  the  eastern  end,  the  little  circle  near  the  mid- 
dle of  the  line  showing  the  place  at  which  the  eclipse 
was  total  at  noon.  The  broken  lines  represent  similar 
data  for  the  annular  eclipses.  This  map  is  one  of  a  se- 
ries prepared  by  the  Austrian  astronomer,  Oppolzer,  show- 
ing the  path  of  every  such  eclipse  from  the  year  1200 


ECLIPSES  115 

B.  c.  to  2160  A.  D.,  a  period  of  more  than  three  thousand 
years. 

If  we  examine  the  dates  of  the  eclipses  shown  in  this 
map  we  shall  find  that  they  are  not  limited  to  the  particu- 
lar seasons,  May  and  N  ovember,  in  which  those  of  the  year 
1900  occurred,  but  are  scattered  through  all  the  months  of 
the  year,  from  January  to  December.  This  shows  at  once 
that  the  line  of  nodes,  N'  N",  of  Fig.  34,  does  not  remain 
in  a  fixed  position,  but  turns  round  in  the  plane  of  the 
earth's  orbit  so  that  in  different  years  the  earth  reaches  the 
node  in  different  months.  The  precession  has  already  fur- 
nished us  an  illustration  of  a  similar  change,  the  slow  rota- 
tion of  the  earth's  axis,  producing  a  corresponding  shifting 
of  the  line  in  which  the  planes  of  the  equator  and  ecliptic 
intersect ;  and  in  much  the  same  way,  through  the  disturb- 
ing influence  of  the  sun's  attraction,  the  line  N'  N"  is  made 
to  revolve  westward,  opposite  to  the  arrowheads  in  Fig. 
34,  at  the  rate  of  nearly  20°  per  year,  so  that  the  earth 
comes  to  each  node  about  19  days  earlier  in  each  year  than 
in  the  year  preceding,  and  the  eclipse  season  in  each  year 
comes  on  the  average  about  19  days  earlier  than  in  the  year 
before,  although  there  is  a  good  deal  of  irregularity  in  the 
amount  of  change  in  particular  years. 

72.  Recurrence  of  eclipses.— Before  the  beginning  of  the 
Christian  era  astronomers  had  found  out  a  rough-and-ready 
method  of  predicting  eclipses,  which  is  still  of  interest  and 
value.  The  substance  of  the  method  is  that  if  we  start 
with  any  eclipse  whatever — e.  g.,  the  eclipse  of  May  28, 1900 
—and  reckon  forward  or  backward  from  that  date  a  period  of 
18  years  and  10  or  11  days,  we  shall  find  another  eclipse  quite 
similar  in  its  general  characteristics  to  the  one  with  Avhich 
we  started.  Thus,  from  the  map  of  eclipses  (Fig.  36),  we 
find  that  a  total  solar  eclipse  will  occur  on  June  8,  1918, 
18  years  and  11  days  after  the  one  illustrated  in  Fig.  35. 
This  period  of  18  years  and  11  days  is  called  saros,  an 
ancient  word  which  means  cycle  or  repetition,  and  since 


116  ASTRONOMY 

every  eclipse  is  repeated  after  the  lapse  of  a  saros,  we  may 
find  the  dates  of  all  the  eclipses  of  1918  by  adding  11 
days  to  the  dates  given  in  the  table  of  eclipses  for  1900 
(§  67),  and  it  is  to  be  especially  noted  that  each  eclipse  of 
1918  will  be  like  its  predecessor  of  1900  in  character — 
lunar,  solar,  partial,  total,  etc.  The  eclipses  of  any  year 
may  be  predicted  by  a  similar  reference  to  those  which 
occurred  eighteen  years  earlier.  Consult  a  file  of  old 
almanacs. 

The  exact  length  of  a  saros  is  223  lunar  months,  each  of 
which  is  a  little  more  than  29.5  days  long,  and.  if  we  multi- 
ply the  exact  value  of  this  last  number  (see  §  60)  by  223, 
we  shall  find  for  the  product  6,585.32  days,  which  is  equal 
to  18  years  11.32  days  when  there  are  four  leap  years  in- 
cluded in  the  18,  or  18  years  10.32  days  when  the  num- 
ber of  leap  years  is  five ;  and  in  applying  the  saros  to  the 
prediction  of  eclipses,  due  heed  must  be  paid  to  the  number 
of  intervening  leap  years.  To  explain  why  eclipses  are 
repeated  at  the  end  of  the  saros,  we  note  that  the  occurrence 
of  an  eclipse  depends  solely  upon  the  relative  positions  of 
the  earth,  moon,  and  node  of  the  moon's  orbit,  and  the 
eclipse  will  be  repeated  as  often  as  these  three  come  back 
to  the  position  which  first  produced  it.  This  happens  at 
the  end  of  every  saros,  since  the  saros  is,  approximately,  the 
least  common  multiple  of  the  length  of  the  year,  the  length 
of  the  lunar  month,  and  the  length  of  time  required  by  the 
line  of  nodes  to  make  a  complete  revolution  around  the 
ecliptic.  If  the  saros  were  exactly  a  multiple  of  these 
three  periods,  every  eclipse  would  be  repeated  over  and 
over  again  for  thousands  of  years ;  but  such  is  not  the 
case,  the  saros  is  not  an  exact  multiple  of  a  year,  nor 
is  it  an  exact  multiple  of  the  time  required  for  a  revo- 
lution of  the  line  of  nodes,  and  in  consequence  the 
restitution  which  comes  at  the  end  of  the  saros  is  not  a 
perfect  one.  The  earth  at  the  223d  new  moon  is  in  fact 
about  half  a  day's  motion  farther  west,  relative  to  the  node, 


ECLIPSES 


117 


than  it  was  at  the  beginning,  and  the  re- 
sulting eclipse,  while  very  similar,  is  not 
precisely  the  same  as  before.  After  another 
18  years,  at  the  second  repetition,  the  earth 
is  a  day  farther  from  the  node  than  at  first, 
and  the  eclipse  differs  still  more  in  charac- 
ter, etc.  This  is  shown  in  Fig.  37,  which 
represents  the  apparent  positions  of  the 
disks  of  the  sun  and  moon  as  seen  from  the 
center  of  the  earth  at  the  end  of  each  sixth 
saros,  108  years,  where  the  upper  row  of 
figures  represents  the  number  of  repetitions 
of  the  eclipse  from  the  beginning,  marked 
0,  to  the  end,  72.  The  solar  eclipse  limits, 
10, 16, 19  days,  are  also  shown,  and  all  those 
eclipses  which  fall  between  the  10-day  lim- 
its will  be  central  as  seen  from  some  part  of 
the  earth,  those  between  16  and  19  partial 
wherever  seen,  while  between  10  and  16 
they  may  be  either  total  or  partial.  Com- 
pare the  figure  with  the  following  descrip- 
tion given  by  Professor  Newcomb  :  "  A  se- 
ries of  such  eclipses  commences  with  a  very 
small  eclipse  near  one  pole  of  the  earth. 
Gradually  increasing  for  about  eleven  recur- 
rences, it  will  become  central  near  the  same 
pole.  Forty  or  more  central  eclipses  will 
then  recur,  the  central  line  moving  slowly 
toward  the  other  pole.  The  series  will  then 
become  partial,  and  finally  cease.  The  en- 
tire duration  of  the  series  will  be  more  than 
a  thousand  years.  A  new  series  commences, 
on  the  average,  at  intervals  of  thirty  years." 
A  similar  figure  may  be  constructed  to 
represent  the  recurrence  of  lunar  eclipses ; 
but  here,  in  consequence  of  the  smaller 


118  ASTRONOMY 

eclipse  limits,  we  shall  find  that  a  series  is  of  shorter  dura- 
tion, a  little  over  eight  centuries  as  compared  with  twelve 
centuries,  which  is  the  average  duration  of  a  series  of  solar 
eclipses. 

One  further  matter  connected  with  the  saros  deserves 
attention.  During  the  period  of  6,585.32  days  the  earth 
has  6,585  times  turned  toward  the  sun  the  same  face  upon 
which  the  moon's  shadow  fell  at  the  beginning  of  the  saros, 
but  at  the  end  of  the  saros  the  odd  0.32  of  a  day  gives  the 
earth  time  to  make  about  a  third  of  a  revolution  more 
before  the  eclipse  is  repeated,  and  in  consequence  the 
eclipse  is  seen  in  a  different  region  of  the  earth,  on  the 
average  about  116°  farther  west  in  longitude.  Compare  in 
Fig.  36  the  regions  in  which  the  eclipses  of  1900  and  1918 
are  visible. 

Is  this  change  in  the  region  where  the  repeated  eclipse 
is  visible,  true  of  lunar  eclipses  as  well  as  solar  ? 

73.  Use  of  eclipses.— At  all  times  and  among  all  peoples 
eclipses,  and  particularly  total  eclipses  of  the  sun,  have 
been  reckoned  among  the  most  impressive  phenomena  of 
Nature.  In  early  times  and  among  uncultivated  people 
they  were  usually  regarded  with  apprehension,  often  amount- 
ing to  a  terror  and  frenzy,  which  civilized  travelers  have 
not  scrupled  to  use  for  their  own  purposes  with  the  aid  of 
the  eclipse  predictions  contained  in  their  almanacs,  threat- 
ening at  the  proper  time  to  destroy  the  sun  or  moon,  and 
pointing  to  the  advancing  eclipse  as  proof  that  their 
threats  were  not  vain.  In  our  own  day  and  our  own  land 
these  feelings  of  awe  have  not  quite  disappeared,  but  for 
the  most  part  eclipses  are  now  awaited  with  an  interest  and 
pleasure  which,  contrasted  with  the.  former  feelings  of  man- 
kind, furnish  one  of  the  most  striking  illustrations  of  the 
effect  of  scientific  knowledge  in  transforming  human  fear 
and  misery  into  a  sense  of  security  and  enjoyment. 

But  to  the  astronomer  an  eclipse  is  more  than  a  beau- 
tiful illustration  of  the  working  of  natural  laws ;  it  is  in 


ECLIPSES  119 

varying  degree  an  opportunity  of  adding  to  his  store  of 
knowledge  respecting  the  heavenly  bodies.  The  region 
immediately  surrounding  the  sun  is  at  most  times  closed  to 
research  by  the  blinding  glare  of  the  sun's  own  light,  so 
that  a  planet  as  large  as  the  moon  might  exist  here  unseen 
were  it  not  for  the  occasional  opportunity  presented  by  a 
total  eclipse  which  shuts  off  the  excessive  light  and  permits 
not  only  a  search  for  unknown  planets  but  for  anything 
and  everything  which  may  exist  around  the  sun.  More 
than  one  astronomer  has  reported  the  discovery  of  such 
planets,  and  at  least  one  of  these  has  found  a  name  and  a 
description  in  some  of  the  books,  but  at  the  present  time 
most  astronomers  are  very  skeptical  about  the  existence  of 
any  such  object  of  considerable  size,  although  there  is 
some  reason  to  believe  that  an  enormous  number  of  little 
bodies,  ranging  in  size  from  grains  of  sand  upward,  do 
move  in  this  region,  as  yet  unseen  and  offering  to  the 
future  problems  for  investigation. 

But  in  other  directions  the  study  of  this  region  at  the 
times  of  total  eclipse  has  yielded  far  larger  returns,  and  in 
the  chapter  on  the  sun  we  shall  have  to  consider  the  mar- 
velous appearances  presented  by  the  solar  prominences  and 
by  the  corona,  an  appendage  of  the  sun  which  reaches  out 
from  his  surface  for  millions  of  miles  but  is  never  seen 
save  at  an  eclipse.  Photographs  of  the  corona  are  taken 
by  astronomers  at  every  opportunity,  and  reproductions  of 
some  of  these  may  be  found  in  Chapter  X. 

Annular  eclipses  and  lunar  eclipses  are  of  comparatively 
little  consequence,  but  any  recorded  eclipse  may  become  of 
value  in  connection  with  chronology.  We  date  our  letters 
in  a  particular  year  of  the  twentieth  century,  and  commonly 
suppose  that  the  years  are  reckoned  from  the  birth  of 
Christ ;  but  this  is  an  error,  for  the  eclipses  which  were  ob- 
served of  old  and  by  the  chroniclers  have  been  associated 
with  events  of  his  life,  when  examined  by  the  astronomers 
are  found  quite  inconsistent  with  astronomic  theory. 


120  ASTRONOMY 

They  are,  however,  reconciled  with  it  if  we  assume  that  our 
system  of  dates  has  its  origin  four  years  after  the  birth  of 
Christ,  or,  in  other  words,  that  Christ  was  born  in  the 
year  4  B.  c.  A  mistake  was  doubtless  made  at  £he  time 
the  Christian  era  was  introduced  into  chronology.  At 
many  other  points  the  chance  record  of  an  eclipse  in 
the  early  annals  of  civilization  furnishes  a  similar  means  of 
controlling  and  correcting  the  dates  assigned  by  the  histo- 
rian to  events  long  past. 


CHAPTEE   VIII 

INSTRUMENTS    AND    THE    PRINCIPLES    INVOLVED 
IN    THEIR    USE 

74.  Two  familiar  instruments. — In  previous  chapters  we 
have  seen  that  a  clock  and  a  divided  circle  (protractor)  are 
needed  for  the  observations  which  an  astronomer  makes, 
and  it  is  worth  while  to  note  here  that  the  geography  of 
the  sky  and  the  science  of  celestial  motions  depend  funda- 
mentally upon  these  two  instruments.  The  protractor  is  a 
simple  instrument,  a  humble  member  of  the  family  of 
divided  circles,  but  untold  labor  and  ingenuity  have  been 
expended  on  this  family  to  make  possible  the  construction 
of  a  circle  so  accurately  divided  that  with  it  angles  may  be 
measured  to  the  tenth  of  a  second  instead  of  to  the  tenth 
of  a  degree — i.  e.,  3,600  times  as  accurate  as  the  protractor 
furnishes. 

The  building  of  a  good  clock  is  equally  important  and 
has  cost  a  like  amount  of  labor  and  pains,  so  that  it  is  a  far 
cry  from  Galileo  and  his  discovery  that  a  pendulum  "  keeps 
time  "  to  the  modern  clock  with  its  accurate  construction 
and  elaborate  provision  against  disturbing  influences  of 
every  kind.  Every  such  timepiece,  whether  it  be  of  the 
nutmeg  variety  which  sells  for  a  dollar,  or  whether  it  be  the 
standard  clock  of  a  great  national  observatory,  is  made  up 
of  the  same  essential  parts  which  fall  naturally  into  four 
classes,  which  we  may  compare  with  the  departments  of  a 
well-ordered  factory :  I.  A  timekeeping  department,  the 
pendulum  or  balance  spring,  whose  oscillations  must  all  be 
of  equal  duration.  II.  A  power  department,  the  weights  or 
9  121 


122  ASTRONOMY 

mainspring,  which,  when  wound,  store  up  the  power  applied 
from  outside  and  give  it  out  piecemeal  as  required  to  keep 
the  first  department  running.  III.  A  publication  depart- 
ment, the  dial  and  hands,  which  give  out  the  time  furnish- 
ed by  Department  I.  IV.  A  transportation  department, 
the  wheels,  which  connect  the  other  three  and  serve  as  a 
means  of  transmitting  power  and  time  from  one  to  the 
other.  The  case  of  either  clock  or  watch  is  merely  the 
roof  which  shelters  it  and  forms  no  department  of  its  in- 
dustry. Of  these  departments  the  first  is  by  far  the  most 
important,  and  its  good  or  bad  performance  makes  or  mars 
the  credit  of  the  clock.  Beware  of  meddling  with  the 
balance  wheel  of  your  watch. 

75.  Radiant  energy, — But  we  have  now  to  consider  other 
instruments  which  in  practice  supplement  or  displace  the 
simple  apparatus  hitherto  employed.  Among  the  most  im- 
portant of  these  modern  instruments  are  the  telescope,  the 
spectroscope,  and  the  photographic  camera ;  and  since  all 
these  instruments  deal  with  the  light  which  comes  from 
the  stars  to  the  earth,  we  must  for  their  proper  understand- 
ing take  account  of  the  nature  of  that  light,  or,  more  strictly 
speaking,  we  must  take  account  of  the  radiant  energy  emit- 
ted by  the  sun  and  stars,  which  energy,  coming  from  the 
sun,  is  translated  by  our  nerves  into  the  two  different  sen- 
sations of  light  and  heat.  The  radiant  energy  which  comes 
from  the  stars  is  not  fundamentally  different  from  that  of 
the  sun,  but  the  amount  of  energy  furnished  by  any  star  is 
so  small  that  it  is  unable  to  produce  through  our  nerves 
any  sensible  perception  of  heat,  and  for  the  same  reason 
the  vast  majority  of  stars  are  invisible  to  the  unaided  eye ; 
they  do  not  furnish  a  sufficient  amount  of  energy  to  affect 
the  optic  nerves.  A  hot  brick  taken  into  the  hand  reveals 
its  presence  by  the  two  different  sensations  of  heat  and 
pressure  (weight) ;  but  as  there  is  only  one  brick  to  produce 
the  two  sensations,  so  there  is  only  one  energy  to  produce 
through  its  action  upon  different  nerves  the  two  sensations 


INSTRUMENTS  USED  AND  PRINCIPLES  INVOLVED     123 

of  light  and  heat,  and  this  energy  is  called  radiant  because 
it  appears  to  stream  forth  radially  from  everything  which 
has  the  capacity  of  emitting  it.  For  the  detailed  study 
of  radiant  energy  the  student  is  referred  to  that  branch 
of  science  called  physics  ;  but  some  of  its  elementary  prin- 
ciples may  be  learned  through  the  following  simple  experi- 
ment, which  the  student  should  not  fail  to  perform  for 
himself : 

Drop  a  bullet  or  other  similar  object  into  a  bucket 
of  water  and  observe  the  circular  waves  which  spread 
from  the  place  where  it  enters  the  water.  These  waves 
are  a  form  of  radiant  energy,  but  differing  from  light  or 
heat  in  that  they  are  visibly  confined  to  a  single  plane, 
the  surface  of  the  water,  instead  of  filling  the  entire  sur- 
rounding space.  By  varying  the  size  of  the  bucket,  the 
depth  of  the  water,  the  weight  of  the  bullet,  etc.,  differ- 
ent kinds  of  waves,  big  and  little,  may  be  produced ;  but 
every  such  set  of  waves  may  be  described  and  defined  in 
all  its  principal  characteristics  by  means  of  three  num- 
bers— viz.,  the  vertical  height  of  the  waves  from  hollow 
to  crest ;  the  distance  of  one  wave  from  the  next ;  and 
the  velocity  with  which  the  waves  travel  across  the  water. 
The  last  of  these  quantities  is  called  the  velocity  of  propa- 
gation ;  the  second  is  called  the  wave  length ;  one  half 
of  the  first  is  called  the  amplitude ;  and  all  these  terms 
find  important  applications  in  the  theory  of  light  and 
heat. 

The  energy  of  the  falling  bullet,  the  disturbance  which 
it  produced  on  entering  the  water,  was  carried  by  the 
waves  from  the  center  to  the  edge  of  the  bucket  but  not 
beyond,  for  the  wave  can  go  only  so  far  as  the  water 
extends.  The  transfer  of  energy  in  this  way  requires  a 
perfectly  continuous  medium  through  which  the  waves 
may  travel,  and  the  whole  visible  universe  is  supposed  to 
be  filled  with  something  called  ether,  which  serves  every- 
where as  a  medium  for  the  transmission  of  radiant  energy 


124  ASTRONOMY 

just  as  the  water  in  the  experiment  served  as  a  medium 
for  transmitting  in  waves  the  energy  furnished  to  it  by  the 
falling  bullet.  The  student  may  think  of  this  energy  as  be- 
ing transmitted  in  spherical  waves  through  the  ether,  every 
glowing  body,  such  as  a  star,  a  candle  flame,  an  arc  lamp,  a 
hot  coal,  etc.,  being  the  origin  and  center  of  such  systems 
of  waves,  and  determining  by  its  own  physical  and  chem- 
ical properties  the  wave  length  and  amplitude  of  the  wave 
systems  given  off. 

The  intensity  of  any  light  depends  upon  the  amplitude 
of  the  corresponding  vibration,  and  its  color  depends  upon 
the  wave  length.  By  ingenious  devices  which  need  not  be 
here  described  it  has  been  found  possible  to  measure  the 
wave  length  corresponding  to  different  colors — e.  g.,  all  of 
the  colors  of  the  rainbow,  and  some  of  these  wave  lengths 
expressed  in  tenth  meters  are  as  follows  :  A  tenth  meter  is 
the  length  obtained  by  dividing  a  meter  into  1010  equal 
parts.  1010  =  10,000,000,000. 

Color.  Wave  length. 

Extreme  limit  of  visible  violet 3.900 

Middle  of  the  violet : 4,060 

blue 4,730 

green 5,270 

yellow 5,810 

orange 5,970 

red 7,000 

Extreme  limit  of  visible  red 7,600 

The  phrase  "  extreme  limit  of  visible  violet "  or  red 
used  above  must  be  understood  to  mean  that  in  general  the 
eye  is  not  able  to  detect  radiant  energy  having  a  wave 
length  less  than  3,900  or  greater  than  7,600  tenth  meters. 
Radiant  energy,  however,  exists  in  waves  of  both  greater 
and  shorter  length  than  the  above,  and  may  be  readily 
detected  by  apparatus  not  subject  to  the  limitations  of  the 
human  eye — e.  g.,  a  common  thermometer  will  show  a  rise 
of  temperature  when  its  bulb  is  exposed  to  radiant  energy 
of  wave  length  much  greater  than  7,600  tenth  meters,  and 


PLATE   I. 


THE  NOETHEEN 


CONSTELLATIONS 


31 


INSTRUMENTS  USED  AND  PRINCIPLES  INVOLVED    125 

a  photographic  plate  will  be  strongly  affected  by  energy  of 
shorter  wave  length  than  3,900  tenth  meters. 

76.  Reflection  and  condensation  of  waves.— When  the 
waves  produced  by  dropping  a  bullet  into  a  bucket  of 
water  meet  the  sides  of  the  bucket,  they  appear  to  rebound 
and  are  reflected  back  toward  the  center,  and  if  the  bullet  is 
dropped  very  near  the  center  of  the  bucket  the  reflected 
waves  will  meet  simultaneously  at  this  point  and  produce 
there  by  their  combined  action  a  wave  higher  than  that 
which  was  reflected  at  the  walls  of  the  bucket.  There  has 
been  a  condensation  of  energy  produced  by  the  reflection, 
and  this  increased  energy  is  shown  by  the  greater  amplitude 
of  the  wave.  The  student  should  not  fail  to  notice  that 
each  portion  of  the  wave  has  traveled  out  and  back  over 
the  radius  of  the  bucket,  and  that  they  meet  simultaneously 
at  the  center  because  of  this  equality  of  the  paths  over  which 
they  travel,  and  the  resulting  equality  of  time  required  to 
go  out  and  back.  If  the  bullet  were  dropped  at  one  side  of 
the  center,  would  the  reflected  waves  produce  at  any  point 
a  condensation  of  energy  ? 

If  the  bucket  were  of  elliptical  instead  of  circular  cross 
section  and  the  bullet  were  dropped  at  one  focus  of  the 
ellipse  there  would  be  produced  a  condensation  of  reflected 
energy  at  the  other  focus,  since  the  sum  of  the  paths  trav- 
ersed by  each  portion  of  the  wave  before  and  after  reflec- 
tion is  equal  to  the  sum  of  the  paths  traversed  by  every 
other  portion,  and  all  parts  of  the  wave  reach  the  second 
focus  at  the  same  time.  Upon  what  geometrical  principle 
does  this  depend  ? 

The  condensation  of  wave  energy  in  the  circular  and 
elliptical  buckets  are  special  cases  under  the  general  prin- 
ciple that  such  a  condensation  will  be  produced  at  any 
point  which  is  so  placed  that  different  parts  of  the  wave 
front  reach  it  simultaneously,  whether  by  reflection  or  by 
some  other  means,  as  shown  below. 

The  student  will  note  that  for  the  sake  of  greater  pre- 


126  ASTRONOMY 

cision  we  here  say  wave  front  instead  of  wave.  If  in  any 
wave  we  imagine  a  line  drawn  along  the  crest,  so  as  to  touch 
every  drop  which  at  that  moment  is  exactly  at  the  crest,  we 
shall  have  what  is  called  a  wave  front,  and  similarly  a  line 
drawn  through  the  trough  between  two  waves,  or  through 
any  set  of  drops  similarly  placed  on  a  wave,  constitutes  a 
wave  front. 

77.  Mirrors  and  lenses. — That  form  of  radiant  energy 
which  we  recognize  as  light  and  heat  may  be  reflected  and 
condensed  precisely  as  are  the  waves  of  water  in  the  exer- 
cise considered  above,  but  owing  to  the  extreme  shortness 
of  the  wave  length  in  this  case  the  reflecting  surface  should 
be  very  smooth  and  highly  polished.  A  piece  of  glass  hol- 
lowed out  in  the  center  by  grinding,  and  with  a  light  film 
of  silver  chemically  deposited  upon  the  hollow  surface  and 
carefully  polished,  is  often  used  by  astronomers  for  this  pur- 
pose, and  is  called  a  concave  mirror. 

The  radiant  energy  coming  from  a  star  or  other  distant 
object  and  falling  upon  the  silvered  face  of  such  a  mirror 
is  reflected  and  condensed  at  a  point  a  little  in  front  of  the 
mirror,  and  there  forms  an  image  of  the  star,  which  may  be 
seen  with  the  unaided  eye,  if  it  is  held  in  the  right  place,  or 
may  be  examined  through  a  magnifying  glass.  Similarly, 
an  image  of  the  sun,  a  planet,  or  a  distant  terrestrial  object 
is  formed  by  the  mirror,  which  condenses  at  its  appropriate 
place  the  radiant  energy  proceeding  from  each  and  every 
point  in  the  surface  of  the  object,  and  this,  in  common 
phrase,  produces  an  image  of  the  object. 

Another  device  more  frequently  used  by  astronomers 
for  the  production  of  images  (condensation  of  energy)  is  a 
lens  which  in  its  simplest  form  is  a  round  piece  of  glass, 
thick  in  the  center  and  thin  at  the  edge,  with  a  cross  sec- 
tion, such  as  is  shown  at  A  B  in  Fig.  38.  If  we  suppose 
E  G  D  to  represent  a  small  part  of  a  wave  front  coming  from 
a  very  distant  source  of  radiant  energy,  such  as  a  star,  this 
wave  front  will  be  practically  a  plane  surface  represented 


INSTRUMENTS  USED  AND  PRINCIPLES  INVOLVED     127 

by  the  straight  line  ED,  but  in  passing  through  the  lens 
this  surface  will  become  warped,  since  light  travels  slower 
in  glass  than  in  air,  and  the  central  part  of  the  beam,  0, 
in  its  onward  motion  will  be  retarded  by  the  thick  center 


FIG.  38.— Illustrating  the  theory  of  lenses. 

of  the  lens,  more  than  E  or  D  will  be  retarded  by  the  com- 
paratively thin  outer  edges  of  A  B.  On  the  right  of  the 
lens  the  wave  front  therefore  will  be  transformed  into  a 
curved  surface  whose  exact  character  depends  upon  the 
shape  of  the  lens  and  the  kind  of  glass  of  which  it  is  made. 
By  properly  choosing  these  the  new  wave  front  may  be 
made  a  part  of  a  sphere  having  its  center  at  the  point  F  and 
the  whole  energy  of  the  wave  front,  E  G  D,  will  then  be  con- 
densed at  F,  because  this  point  is  equally  distant  from  all 
parts  of  the  warped  wave  front,  and  therefore  is  in  a  posi- 
tion to  receive  them  simultaneously.  The  distance  of  F 
from  A  B  is  called  the  focal  length  of  the  lens,  and  ^itself 
is  called  the  focus.  The  significance  of  this  last  word 
(Latin,  focus  =  fireplace)  will  become  painfully  apparent  to 
the  student  if  he  will  hold  a  common  reading  glass  between 
his  hand  and  the  sun  in  such  a  way  that  the  focus  falls 
upon  his  hand. 

All  the  energy  transmitted  by  the  lens  in  the  direc- 
tion GFis  concentrated  upon  a  very  small  area  at  F,  and 
an  image  of  the  object — e.  g.,  a  star,  from  which  the  light 
came — is  formed  here.  Other  stars  situated  near  the  one  in 
question  will  also  send  beams  of  light  along  slightly  differ- 
ent directions  to  the  lens,  and  these  will  be  concentrated, 
each  in  its  appropriate  place,  in  the  focal  plane,  F H,  passed 
through  the  focus,  F,  perpendicular  to  the  line,  F  G,  and 


128 


ASTRONOMY 


we  shall  find  in  this  plane  a  picture  of  all  the  stars  or  other 
objects  within  the  range  of  the  lens. 

78.  Telescopes. — The  simplest  kind  of  telescope  consists 
of  a  concave  mirror  to  produce  images,  and  a  magnifying 
glass,  called  an  eyepiece,  through  which  to  examine  them ; 

but  for  convenience' 
sake,  so  that  the  observ- 
er may  not  stand  in  his 
own  light,  a  small  mir- 
ror is  frequently  added 
to  this  combination,  as 
at  H  in  Fig.  39,  where 
the  lines  represent  the 
directions  along  which 
the  energy  is  propagated. 
By  reflection  from  this  mirror  the  focal  plane  and  the 
images  are  shifted  to  F,  where  they  may  be  examined  from 
one  side  through  the  magnifying  glass  E. 

Such  a  combination  of  parts  is  called  a  reflecting  tele- 
scope, while  one  in  which  the  images  are  produced  by  a 
lens  or  combination  of  lenses  is  called  a  refracting  tele- 
scope, the  adjective  having  reference  to  the  bending,  re- 
fraction, produced  by  the  glass  upon  the  direction  in  which 
the  energy  is  propagated.  The  customary  arrangement  of 
parts  in  such  a  telescope  is  shown  in  Fig.  40,  where  the 


FIG. 


). — Essential  parts  of 
telescope. 


reflecting 


FIG.  40.— A  simple  form  of  refracting  telescope. 

part  marked  0  is  called  the  objective  and  V  E  (the  mag- 
nifying glass)  is  the  eyepiece,  or  ocular,  as  it  is  sometimes 
called. 

Most   objects  with  which  we  have  to  deal  in  using  a 
telescope  send  to  it  not  light  of  one  color  only,  but  a  mix- 


INSTRUMENTS  USED  AND  PRINCIPLES  INVOLVED     129 

ture  of  light  of  many  colors,  many  different  wave  lengths, 
some  of  which  are  refracted  more  than  others  by  the  glass 
of  which  the  lens  is  composed,  and  in  consequence  of  these 
different  amounts  of  refraction  a  single  lens  does  not  fur- 
nish a  single  image  of  a  star,  but  gives  a  confused  jumble  of 
red  and  yellow  and  blue  images  much  inferior  in  sharpness 
of  outline  (definition)  to  the  images  made  by  a  good  con- 
cave mirror.  To  remedy  this  defect  it  is  customary  to 
make  the  objective  of  two  or  more  pieces  of  glass  of  differ- 
ent densities  and  ground  to  different  shapes  as  is  shown  at  0 
in  Fig.  40.  The  two  pieces  of  glass  thus  mounted  in  one 
frame  constitute  a  compound  lens  having  its  own  focal 
plane,  shown  at  F  in  the  figure,  and  similarly  the  lenses 
composing  the  eyepiece  have  a  focal  plane  between  the 
eyepiece  and  the  objective  which  must  also  fall  at  F,  and 
in  the  use  of  a  telescope  the  eyepiece  must  be  pushed  out 
or  in  until  its  focal  plane  coincides  with  that  of  the  objec- 
tive. This  process,  which  is  called  focusing,  is  what  is 
accomplished  in  the  ordinary  opera  glass  by  turning  a  screw 
placed  between  the  two  tubes,  and  it  must  be  carefully 
done  with  every  telescope  in  order  to  obtain  distinct  vision. 
79.  Magnifying  power.— The  amount  by  which  a  given 
telescope  magnifies  depends  upon  the  focal  length  of  the  ob- 
jective (or  mirror)  and  the  focal  length  of  the  eyepiece,  and 
is  equal  to  the  ratio  of  these  two  quantities.  Thus  in  lig. 
40  the  distance  of  the  objective  from  the  focal  plane  J^is 
about  16  times  as  great  as  the  distance  of  the  eyepiece 
from  the  same  plane,  and  the  magnifying  power  of  this 
telescope  is  therefore  16  diameters.  A  magnifying  power 
of  16  diameters  means  that  the  diameter  of  any  object  seen 
in  the  telescope  looks  16  times  as  large  as  it  appears  with- 
out the  telescope,  and  is  nearly  equivalent  to  saying  that 
the  object  appears  only  one  sixteenth  as  far  off.  Some- 
times the  magnifying  power  is  assumed  to  be  the  number 
of  times  that  the  area  of  an  object  seems  increased ;  and 
since  areas  are  proportional  to  the  squares  of  lines,  the 


130  ASTRONOMY 

magnifying  power  of  16  diameters  might  be  called  a  power 
of  256.  Every  large  telescope  is  provided  with  several  eye- 
pieces of  different  focal  lengths,  ranging  from  a  quarter  of 
an  inch  to  two  and  a  half  inches,  which  are  used  to  fur- 
nish different  magnifying  powers  as  may  be  required  for 
the  different  kinds  of  work  undertaken  with  the  instru- 
ment. Higher  powers  can  be  used  with  large  telescopes 
than  with  small  ones,  but  it  is  seldom  advantageous  to 
use  with  any  telescope  an  eyepiece  giving  a  higher  power 
than  60  diameters  for  each  inch  of  diameter  of  the  ob- 
jective. 

The  part  played  by  the  eyepiece  in  determining  magni- 
fying power  will  be  readily  understood  from  the  following 
experiment : 

Make  a  pin  hole  in  a  piece  of  cardboard.  Bring  a 
printed  page  so  close  to  one  eye  that  you  can  no  longer  see 
the  letters  distinctly,  and  then  place  the  pin  hole  between 
the  eye  and  the  page.  The  letters  which  were  before 
blurred  may  now  be  seen  plainly  through  the  pin  hole, 
even  when  the  page  is  brought  nearer  to  the  eye  than  be- 
fore. As  it  is  brought  nearer,  notice  how  the  letters  seem 
to  become  larger,  solely  because  they  are  nearer.  A  pin 
hole  is  the  simplest  kind  of  a  magnifier,  and  the  eyepiece 
in  a  telescope  plays  the  same  part  as  does  the  pin  hole  in 
the  experiment ;  it  enables  the  eye  to  be  brought  nearer  to 
the  image,  and  the  shorter  the  focal  length  of  the  eyepiece 
the  nearer  is  the  eye  brought  to  the  image  and  the  higher 
is  the  magnifying  power. 

80.  The  equatorial  mounting,— Telescopes  are  of  all  sizes, 
from  the  modest  opera  glass  which  may  be  carried  in  the 
pocket  and  which  requires  no  other  support  than  the  hand, 
to  the  giant  which  must  have  a  special  roof  to  shelter  it 
and  elaborate  machinery  to  support  and  direct  it  toward 
the  sky.  But  for  even  the  largest  telescopes  this  machinery 
consists  of  the  following  parts,  which  are  illustrated,  with 
exception  of  the  last  one,  in  the  small  equatorial  telescope 


INSTRUMENTS  USED  AND  PRINCIPLES  INVOLVED     131 

shown  in  Fig.  41.  It  is  not  customary  to  place  a  driving 
clock  on  so  small  a  telescope  as  this  : 

(a)  A  supporting  pier  or  tripod. 

(b)  An  axis  placed  parallel  to  the  axis  of  the  earth. 

(c)  Another  axis  at 
right  angles  to  b  and 
capable    of    revolving 
upon  b  as  an  axle. 

(d)  The    telescope 
tube  attached  to  c  and  ca- 
pable of  revolving  about  c. 

(e)  Graduated      circles 
attached    to    c    and    d  to 
measure    the    amount    by 
which    the     telescope     is 
turned  on  these  axes. 

(/)  A  driving  clock  so 
connected  with  b  as  to 
make  c  (and  d)  revolve 
about  b  with  an  angular 
velocity  equal  and  opposite 
to  that  with  which  the 
earth  turns  upon  its  axis. 

Such  a  support  is  called 
an  equatorial  mounting, 
and  the  student  should 
note  from  the  figure  that 
the  circles,  e,  measure  the 
hour  angle  and  declination 
of  any  star  toward  which  FlG  41  _A  simp7e  eqn^orial  mounting. 
the  telescope  is  directed, 

and  conversely  if  the  telescope  be  so  set  that  these  circles 
indicate  the  hour  angle  and  declination  of  any  given  star, 
the  telescope  will  then  point  toward  that  star.  In  this 
way  it  is  easy  to  find  with  the  telescope  any  moderately 
bright  star,  even  in  broad  daylight,  although  it  is  then 


INSTRUMENTS  USED  AND  PRINCIPLES  INVOLVED     133 


absolutely  invisible  to  the  naked  eye.  The  rotation  of  the 
earth  about  its  axis  will  speedily  carry  the  telescope  away 
from  the  star,  but  if  the  driving  clock  be  started,  its  effect 
is  to  turn  the  telescope  toward  the  west  just  as  fast  as  the 
earth's  rotation  carries  it  toward  the  east,  and  by  these 
compensating  motions 
to  keep  it  directed  to- 
ward the  star.  In  Fig. 
42,  which  represents 
the  largest  and  one  of 
the  most  perfect  re- 
fracting telescopes 
ever  built,  let  the  stu- 
dent pick  out  and  iden- 
tify the  several  parts 
of  the  mounting  above 
described.  A  part  of 
the  driving  clock  may 
be  seen  within  the  head 
of  the  pier.  In  Fig. 
43  trace  out  the  cor- 
responding parts  in 
the  mounting  of  a  re- 
flecting telescope. 

A  telescope  is  often 
only  a  subordinate  part 
of  some  instrument  or 
apparatus,  and  then  its 
style  of  mounting  is 
determined  by  the  requirements  of  the  special  case ;  but 
when  the  telescope  is  the  chief  thing,  and  the  remainder 
of  the  apparatus  is  subordinate  to  it,  the  equatorial  mount- 
ing is  almost  always  adopted,  although  sometimes  the  ar- 
rangement of  the  parts  is  very  different  in  appearance  from 
any  of  those  shown  above.  Beware  of  the  popular  error  that 
an  object  held  close  in  front  of  a  telescope  can  be  seen  by  an 


FIG.  43.— The  reflecting  telescope  of  the 
Paris  Observatory. 


134 


ASTRONOMY 


observer  at  the  eyepiece.     The  numerous  stories  of  astrono- 
mers who  saw  spiders  crawling  over  the  objective  of  their 
telescope,  and  imagined  they  were  beholding  strange  ob- 
jects in  the  sky,  are  all  fictitious,  since  nothing  on  or  near 
the  objective  could  possibly  be  seen  through  the  telescope. 
81.  Photography. — A  photographic  camera  consists  of  a 
lens  and  a  device  for  holding  at  its  focus  a  specially  pre- 
pared plate  or  film.  This 
plate  carries  a  chemical 
deposit   which    is    very 
sensitive  to   the  action 
of  light,  and  which  may 
be  made  to  preserve  the 
imprint  of  any  picture 
which   the   lens    forms 
upon  it.     If  such  a  sen- 
sitive plate  is  placed  at 
the  focus  of  a  reflecting 
telescope,  the  combina- 
tion becomes  a  camera 
available  for   astronom- 
ical photography,  and  at 
the    present    time    the 
tendency   is    strong  in 
nearly  every  branch  of 
astronomical  research  to 
substitute  the  sensitive 
plate  in  place  of  the  ob- 
server at  a  telescope.    A 
refracting  telescope  may  also  be  used  for  astronomical  pho- 
tography, and  is  very  much  used,  but  some  complications 
occur  here  on  account  of  the  resolution  of  the  light  into 
its  constituent  colors  in    passing  through    the   objective. 
Fig.  44  shows  such  a  telescope,  or  rather  two  telescopes,  one 
photographic,  the  other  visual,  supported  side  by  side  upon 
the  same  equatorial  mounting. 


FIG.  44.— Photographic  telescope  of  the  Paris 
Observatory. 


INSTRUMENTS  USED  AND  PRINCIPLES  INVOLVED     135 

One  of  the  great  advantages  of  photography  is  found  in 
connection  with  what  is  called — 

82.  Personal  equation, — It  is  a  remarkable  fact,  first  in- 
vestigated by  the  German  astronomer  Bessel,  three  quar- 
ters of  a  century  ago,  that  where  extreme  accuracy  is  re- 
quired the  human  senses  can  not  be  implicitly  relied  upon. 
The  most  skillful  observers  will  not  agree  exactly  in  their 
measurement  of  an  angle  or  in  estimating  the  exact  instant 
at  which  a  star  crossed  the  meridian ;  the  most  skillful 
artists   can  not  draw  identical  pictures  of  the  same  ob- 
ject, etc. 

These  minor  deceptions  of  the  senses  are  included  in 
the  term  personal  equation,  which  is  a  famous  phrase  in 
astronomy,  denoting  that  the  observations  of  any  given 
person  require  to  be  corrected  by  means  of  some  equation 
involving  his  personality. 

General  health,  digestion,  nerves,  fatigue,  all  influence 
the  personal  equation,  and  it  was  in  reference  to  such  mat- 
ters that  one  of  the  most  eminent  of  living  astronomers  has 
given  this  description  of  his  habits  of  observing : 

"  In  order  to  avoid  every  physiological  disturbance,  I 
"~Tiave  adopted  the  rule  to  abstain  for  one  or  two  hours  be- 
fore commencing  observations  from  every  laborious  occupa- 
tion ;  never  to  go  to  the  telescope  with  stomach  loaded  with 
food ;  to  abstain  from  everything  which  could  affect  the 
nervous  system,  from  narcotics  and  alcohol,  and  especially 
from  the  abuse  of  coffee,  which  I  have  found  to  be  exceed- 
ingly prejudicial  to  the  accuracy  of  observation."*  A 
regimen  suggestive  of  preparation  for  an  athletic  contest 
thanj&rthe  more  quiet  labors  of  an  astronomer. 

83.  Visual  and  photographic  work. — The   photographic 
plate  has  no  stomach  and  no  nerves,  and  is  thus  free  from 
many  of  the  sources  of  error  which  inhere  in  visual  observa- 
tions, and  in  special  classes  of  work   it  possesses   other 

*  Schiaparelli,  Osservazioni  sulle  Stelle  Doppie. 


136  ASTRONOMY 

marked  advantages,  such  as  rapidity  when  many  stars  are 
to  he  dealt  with  simultaneously,  permanence  of  record,  and 
owing  to  the  cumulative  effect  of  long  exposure  of  the  plate 
it  is  possible  to  photograph  with  a  given  telescope  stars  far 
too  faint  to  be  seen  through  it.  On  the  other  hand,  the 
eye  has  the  advantage  in  some  respects,  such  as  studying 
the  minute  details  of  a  fairly  bright  object — e.  g.,  the  sur- 
face of  a  planet,  or  the  sun's  corona  and,  for  the  present  at 
least,  neither  method  of  observing  can  exclude  the  other. 
For  a  remarkable  case  of  discordance  between  the  results 
of  photographic  and  visual  observations  compare  the  pic- 
tures of  the  great  nebula  in  the  constellation  Andromeda, 
which  are  given  in  Chapter  XIV.  A  partial  explanation 
of  these  discordances  and  other  similar  ones  is  that  the 
eye  is  most  strongly  affected  by  greenish-yellow  light, 
while  the  photographic  plate  responds  most  strongly  to 
violet  light ;  the  photograph,  therefore,  represents  things 
which  the  eye  has  little  capacity  for  seeing,  and  vice  versa. 
84.  The  spectroscope. — In  some  respects  the  spectroscope 
is  the  exact  counterpart  of  the  telescope.  The  latter  con- 
denses radiant  energy  and  the  former  disperses  it.  As  a 
measuring  instrument  the  telescope  is  mainly  concerned 
with  the  direction  from  which  light  comes,  and  the  differ- 
ent colors  of  which  that  light  is  composed  affect  it  only  as 
an  obstacle  to  be  overcome  in  its  construction.  On  the 
other  hand,  with  the  spectroscope  the  direction  from  which 
the  radiant  energy  comes  is  of  minor  consequence,  and  the 
all-important  consideration  is  the  intrinsic  character  of 
that  radiation.  What  colors  are  present  in  the  light  and 
in  what  proportions  ?  What  can  these  colors  be  made  to 
tell  about  the  nature  and  condition  of  the  body  from  which 
they  come,  be  it  sun,  or  star,  or  some  terrestrial  source  of 
light,  such  as  an  arc  lamp,  a  candle  flame,  or  a  furnace  in 
blast  ?  These  are  some  of  the  characteristic  questions  of 
the  spectrum  analysis,  and,  as  the  name  implies,  they  are 
solved  by  analyzing  the  radiant  energy  into  its  component 


INSTRUMENTS  USED  AND  PRINCIPLES  INVOLVED     137 

parts,  setting  down  the  blue  light  in  one  place,  the  yellow 
in  another,  the  red  in  still  another,  etc.,  and  interpreting 
this  array  of  colors  by  means  of  principles  which  we  shall 
have  to  consider.  Something  of  this  process  of  color 
analysis  may  be  seen  in  the  brilliant  hues  shown  by  a  soap 
bubble,  or  reflected  from  a  piece  of  mother-of-pearl,  and 
still  more  strikingly  exhibited  in  the  rainbow,  produced  by 


FIG.  45.— Resolution  of  light  into  its  component  colors. 

raindrops  which  break  up  the  sunlight  into  its  component 
colors  and  arrange  them  each  in  its  appropriate  place. 
Any  of  these  natural  methods  of  decomposing  light  might 
be  employed  in  the  construction  of  a  spectroscope,  but  in 
spectroscopes  which  are  used  for  analyzing  the  light  from 
feeble  sources,  such  as  a  star,  or  a  candle  flame,  a  glass 
prism  of  triangular  cross  section  is  usually  employed  to  re- 
solve the  light  into  its  component  colors,  which  it  does  by 
refracting  it  as  shown  at  the  edges  of  the  lens  in  Fig.  38. 

The  course  of  a  beam  of  light  in  passing  through  such 
a  prism  is  shown  in  Fig.  45.  Note  that  the  bending  of  the 
light  from  its  original  course  into  a  new  one,  which  is  here 
shown  as  produced  by  the  prism,  is  quite  similar  to  the 
bending  shown  at  the  edges  of  a  lens  and  comes  from  the 
10 


138  ASTRONOMY 

same  cause,  the  slower  velocity  of  light  in  glass  than  in 
air.  It  takes  the  light-waves  as  long  to  move  over  the 
path  A  B  in  glass  as  over  the  longer  path  1,  2,  3,  4,  of 
which  only  the  middle  section  lies  in  the  glass. 

'Not  only  does  the  prism  bend  the  beam  of  light  trans- 
mitted by  it,  but  it  bends  in  different  degree  light  of  differ- 
ent colors,  as  is  shown  in  the  figure,  where  the  beam  at  the 
left  of  the  prism  is  supposed  to  be  made  up  of  a  mixture  of 
blue  and  red  light,  while  at  the  right  of  the  prism  the 
greater  deviation  imparted  to  the  blue  quite  separates  the 
colors,  so  that  they  fall  at  different  places  on  the  screen, 
S  S.  The  compound  light  has  been  analyzed  into  its  con- 
stituents, and  in  the  same  way  every  other  color  would  be 
put  down  at  its  appropriate  place  on  the  screen,  and  a  beam 
of  white  light  falling  upon  the  prism  would  be  resolved  by 
it  into  a  sequence  of  colors,  falling  upon  the  screen  in  the 
order  red,  orange,  yellow,  green,  blue,  indigo,  violet.  The 
initial  letters  of  these  names  make  the  word  RoygMv,  and 
by  means  of  it  their  order  is  easily  remembered. 

If  the  light  which  is  to  be  examined  comes  from  a  star 
the  analysis  made  by  the  prism  is  complete,  and  when 
viewed  through  a  telescope  the  image  of  the  star  is  seen  to 
be  drawn  out  into  a  band  of  light,  which  is  called  a  spec- 
trum, and  is  red  at  one  end  and  violet  or  blue  at  the  other, 
with  all  the  colors  of  the  rainbow  intervening  in  proper 
order  between  these  extremes.  Such  a  prism  placed  in 
front  of  the  objective  of  a  telescope  is  called  an  objec- 
tive prism,  and  has  been  used  for  stellar  work  with  marked 
success  at  the  Harvard  College  Observatory.  But  if  the 
light  to  be  analyzed  comes  from  an  object  having  an  ap- 
preciable extent  of  surface,  such  as  the  sun  or  a  planet, 
the  objective  prism  can  not  be  successfully  employed, 
since  each  point  of  the  surface  will  produce  its  own  spec- 
trum, and  these  will  appear  in  the  view  telescope  super- 
posed and  confused  one  with  another  in  a  very  objection- 
able manner.  To  avoid  this  difficulty  there  is  placed 


INSTRUMENTS  USED  AND  PRINCIPLES  INVOLVED     139 

between  the  prism  and  the  source  of  light  an  opaque 
screen,  $,  with  a  very  narrow  slit  cut  in  it,  through  which  all 
the  light  to  be  analyzed  must  pass  and  must  also  go  through 
a  lens,  J,  placed  between  the  slit  and  the  prism,  as  shown 
in  Fig.  46.  The  slit  and  lens,  together  with  the  tube  in 


FIG.  46.— Principal  parts  of  a  spectroscope. 


which  they  are  usually  supported,  are  called  a  collimator, 
By  this  device  a  very  limited  amount  of  light  is  permitted 
to  pass  from  the  object  through  the  slit  and  lens  to  the 
prism  and  is  there  resolved  into  a  spectrum,  which  is  in 
effect  a  series  of  images  of  the  slit  in  light  of  different 
colors,  placed  side  by  side  so  close  as  to  make  practically  a 
continuous  ribbon  of  light  whose  width  is  the  length  of 
each  individual  picture  of  the  slit.  The  length  of  the  ribbon 
(dispersion)  depends  mainly  upon  the  shape  of  the  prism 
and  the  kind  of  glass  of  which  it  is  made,  and  it  may  be 
very  greatly  increased  and  the  efficiency  of  the  spectro- 
scope enhanced  by  putting  two,  three,  or  more  prisms  in 
place  of  the  single  one  above  described.  When  the  amount 
of  light  is  very  great,  as  in  the  case  of  the  sun  or  an  elec- 
tric arc  lamp,  it  is  advantageous  to  alter  slightly  the  ar- 
rangement of  the  spectroscope '  and  to  substitute  in  place 
of  the  prism  a  grating — i.  e.,  a  metallic  mirror  with  a  great 
number  of  fine  parallel  lines  ruled  upon  its  surface  at  equal 
intervals,  one  from  another.  It  is  by  virtue  of  such  a  sys- 
tem of  fine  parallel  grooves  that  mother-of-pearl  displays 


140 


ASTRONOMY 


its  beautiful  color  effects,  and  a  brilliant  spectrum  of  great 
purity  and  high  dispersion  is  furnished  by  a  grating  ruled 
with  from  10,000  to  20,000  lines  to  the  inch.  Fig.  47  rep- 
resents, rather  crudely,  a  part  of  the  spec- 
trum of  an  arc  light  furnished  by  such  a 
grating,  or  rather  it  shows  three  different 
spectra  arranged  side  by  side,  and  looking 
something  like  a  rude  ladder.  The  sides 
of  the  ladder  are  the  spectra  furnished  by 
,  the  incandescent  carbons  of  the  lamp,  and 
the  cross  pieces  are  the  spectrum  of  the 
electric  arc  filling  the  space  between  the 
carbons.  Fig.  48  shows  a  continuation  of 
the  same  spectra  into  a  region  where  the 
radiant  energy  is  invisible  to  the  eye,  but 
is  capable  of  being  photographed. 

It  is  only  when  a  lens  is  placed  be- 
•  tween  the  lamp  and  the  slit  of  the  spec- 
troscope that  the  three  spectra  are  shown 
distinct  from  each  other  as  in  the  figure. 
The  purpose  of  the  lens  is  to  make  a  pic- 
ture of  the  lamp  upon  the  slit,  so  that 
all  the  radiant  energy  from  any  one  point 
of  the  arc  may  be  brought  to  one  part  of 
the  slit,  and  thus  appear  in  the  resulting 
spectrum  separated  from  the  energy 
which  comes  from  every  other  part  of 
the  arc.  Such  an  instrument  is  called 
an  analyzing  spectroscope  while  one  with- 
out the  lens  is  called  an  integrating  spec- 
troscope, since  it  furnishes  to  each  point 
of  the  slit  a  sample  of  the  radiant  energy 
coming  from  every  part  of  the  source  of 
light,  and  thus  produces  only  an  average 
spectrum  of  that  source  without  distinction  of  its  parts. 
When  a  spectroscope  is  attached  to  a  telescope,  as  is  often 


INSTRUMENTS  USED  AND  PRINCIPLES  INVOLVED 

done  (see  Fig.  49),  the  eyepiece  is  removed  to  make  way 
for  it,  and  the  telescope  objective  takes  the  part  of  the 
analyzing  lens.  A  camera  is  frequently  combined  with 


FIG.  48.— Violet  and  ultraviolet  parts  of  spectrum  of  an  arc  lamp. 

such  an  apparatus  to  photograph  the  spectra  it  furnishes, 
and  the  whole  instrument  is  then  called  a  spectrograph. 

85.  Spectrum  analysis, — Having  seen  the  mechanism  of 
the  spectroscope  by  which  the  light  incident  upon  it  is 
resolved  into  its  constituent  parts  and  drawn  out  into  a 
series  of  colors  arranged  in  the  order  of  their  wave  lengths, 
we  have  now  to  consider  the  interpretation  which  is  to  be 
placed  upon  the  various  kinds  of  spectra  which  may  be 
seen,  and  here  we  rely  upon  the  experience  of  physicists 
and  chemists,  from  whom  we  learn  as  follows : 

The  radiant  energy  which  is  analyzed  by  the  spectro- 
scope has  its  source  in  the  atoms  and  molecules  which  make 
up  the  luminous  body  from  which  the  energy  is  radiated, 
and  these  atoms  and  molecules  are  able  to  impress  upon 
the  ether  their  own  peculiarities  in  the  shape  of  waves  of 
different  length  and  amplitude.  We  have  seen  that  by 
varying  the  conditions  of  the  experiment  different  kinds  of 
waves  may  be  produced  in  a  bucket  of  water;  and  as  a 
study  of  these  waves  might  furnish  an  index  to  the  condi- 
tions which  produced  them,  so  the  study  of  the  waves 
peculiar  to  the  light  which  comes  from  any  source  may  be 
made  to  give  information  about  the  molecules  which  make 
up  that  source.  Thus  the  molecules  of  iron  produce  a 
system  of  waves  peculiar  to  themselves  and  which  can  be 
duplicated  by  nothing  else,  and  every  other  substance 
gives  off  its  own  peculiar  type  of  energy,  presenting  a 


142 


ASTRONOMY 


limited  and  definite  number  of  wave  lengths  dependent 
upon  the  nature  and  condition  of  its  molecules.  If  these 
molecules  are  free  to  behave  in  their  own  characteristic 
fashion  without  disturbance  or  crowding,  they  emit  light  of 
these  wave  lengths  only,  and  we  find  in  the  spectrum  a 
series  of  bright  lines,  pictures  of  the  slit  produced  by  light 
of  these  particular  wave  lengths,  while  between  these  bright 
lines  lie  dark  spaces  showing  the  absence  from  the  radiant 
energy  of  light  of  intermediate  wave  lengths.  Such  a 
spectrum  is  shown  in  the  central  portion  of  Fig.  47,  which, 


FIG.  49. — A  spectroscope  attached  to  the  Yerkes  telescope. 

as  we  have  already  seen,  is  produced  by  the  space  between 
the  carbons  of  the  arc  lamp.  On  the  other  hand,  if  the 
molecules  are  closely  packed  together  under  pressure  they 
so  interfere  with  each  other  as  to  give  off  a  jumble  of 
energy  of  all  wave  lengths,  and  this  is  translated  by  the 
spectroscope  into  a  continuous  ribbon  of  light  with  no  dark 
spaces  intervening,  as  in  the  upper  and  lower  parts  of  Figs. 


INSTRUMENTS  USED  AND  PRINCIPLES  INVOLVED    143 

47  and  48,  produced  by  the  incandescent  solid  carbons  of 
the  lamp.  These  two  types  are  known  as  the  continuous 
and  discontinuous  spectrum,  and  we  may  lay  down  the  fol- 
lowing principle  regarding  them  : 

A  discontinuous  spectrum,  or  bright-line  spectrum  as 
it  is  familiarly  called,  indicates  that  the  molecules  of  the 
source  of  light  are  not  crowded  together,  and  therefore  the 
light  must  come  from  an  incandescent  gas.  A  continuous 
spectrum  shows  only  that  the  molecules  are  crowded  to- 
gether, or  are  so  numerous  that  the  body  to  which  they 
belong  is  not  transparent  and  gives  no  further  informa- 
tion. The  body  may  be  solid,  liquid,  or  gaseous,  but  in 
the  latter  case  the  gas  must  be  under  considerable  pres- 
sure or  of  great  extent. 

A  second  principle  is :  The  lines  which  appear  in  a  spec- 
trum are  characteristic  of  the  source  from  which  the  light 
came— e.  g.,  the  double  line  in  the  yellow  part  of  the  spec- 
trum at  the  extreme  left  in  Fig.  47  is  produced  by  sodium 
vapor  in  and  around  the  electric  arc  and  is  never  pro- 
duced by  anything  but  sodium.  When  by  laboratory  ex- 
periments we  have  learned  the  particular  set  of  lines 
corresponding  to  iron,  we  may  treat  the  presence  of  these 
lines  in  another  spectrum  as  proof  that  iron  is  present 
in  the  source  from  which  the  light  came,  whether  that 
source  be  a  white-hot  poker  in  the  next  room  or  a  star 
immeasurably  distant.  The  evidence  that  iron  is  pres- 
ent lies  in  the  nature  of  the  light,  and  there  is  no  reason 
to  suppose  that  nature  to  be  altered  on  the  way  from 
star  to  earth.  It  may,  however,  be  altered  by  something 
happening  to  the  source  from  which  it  comes — e.  g.,  chang- 
ing temperature  or  pressure  may  affect,  and  does  affect,  the 
spectrum  which  such  a  substance  as  iron  emits,  and  we  must 
be  prepared  to  find  the  same  substance  presenting  different 
spectra  under  different  conditions,  only  these  conditions 
must  be  greatly  altered  in  order  to  produce  radical  changes 
in  the  spectrum. 


144 


ASTRONOMY 


86.  Wave  lengths.— To  identi- 
fy a  line  as  belonging  to  and  pro- 
duced by  iron  or  any  other  sub- 
stance, its  position  in  the  spec- 
trum— i.  e.,  its  wave  length — must 
be   very    accurately    determined, 
and  for  the  identification  of  a  sub- 
stance by  means  of  its  spectrum  it 
is  often  necessary  to  determine  ac- 
curately the  wave  lengths  of  many 
lines.      A  complicated   spectrum 
may  consist  of  hundreds  or  thou- 
sands of  lines,  due  to  the  presence 
of  many  different   substances  in 
the   source   of  light,  and  unless 
great  care  is  taken  in  assigning 
the  exact  position  of  these  lines 
in  the  spectrum,  confusion   and 
wrong  identifications  are  sure  to 
result.     For  the  measurement  of 
the  required  wave  length  a  tenth 
meter  (§  75)  is  the  unit  employed, 
and  a  scale  of   wave  lengths  ex- 
pressed in  this  unit  is  presented 
in  Fig.   50.      The  accuracy  with 
which  some  of  these  wave  lengths 
are  determined  is  truly  astound- 
ing ;  a  ten-billionth  of  an  inch ! 
These    numerical    wave    lengths 
save  all  necessity  for  referring  to 
the  color  of  any  part  of  the  spec- 
trum, and  pictures  of  spectra  for 
scientific    use    are    not    usually 
printed  in  colors. 

87.  Absorption  spectra.— There 
is  another  kind  of  spectrum,  of 


INSTRUMENTS  USED  AND  PRINCIPLES  INVOLVED    145 

greater  importance  than  either  of  those  above  considered, 
which  is  well  illustrated  by  the  spectrum  of  sunlight  (Fig. 
50).  This  is  a  nearly  continuous  spectrum  crossed  by  nu- 
merous dark  lines  due  to  absorption  of  radiant  energy  in  a 
comparatively  cool  gas  through  which  it  passes  on  its  way 
to  the  spectroscope.  Fraunhofer,  who  made  the  first  care- 
ful study  of  spectra,  designated  some  of  the  more  conspicu- 
ous of  these  lines  by  letters  of  the  alphabet  which  are  shown 
in  the  plate,  and  which  are  still  in  common  use  as  names 
for  the  lines,  not  only  in  the  spectrum  of  sunlight  but 
wherever  they  occur  in  other  spectra.  Thus  the  double 
line  marked  Z>,  wave  length  5893,  falls  at  precisely  the  same 
place  in  the  spectrum  as  does  the  double  (sodium)  line 
which  we  have  already  seen  in  the  yellow  part  of  the  arc- 
light  spectrum,  which  line  is  also  called  D  and  bears  a  very 
intimate  relation  to  the  dark  D  line  of  the  solar  spectrum. 

The  student  who  has  access  to  colored  crayons  should 
color  one  edge  of  Fig.  50  in  accordance  with  the  lettering 
there  given  and,  so  far  as  possible,  he  should  make  the 
transition  from  one  color  to  the  next  a  gradual  one,  as  it  is 
in  the  rainbow. 

Fig.  50  is  far  from  being  a  complete  representation  of 
the  spectrum  of  sunlight.  Xot  only  does  this  spectrum  ex- 
tend both  to  the  right  and  to  the  left  into  regions  invisible 
to  the  human  eye,  but  within  the  limits  of  the  figure,  in- 
stead of  the  seventy-five  lines  there  shown,  there  are  liter- 
ally thousands  upon  thousands  of  lines,  of  which  only  the 
most  conspicuous  can  be  shown  in  such  a  cut  as  this. 

The  dark  lines  which  appear  in  the  spectrum  of  sun- 
light can,  under  proper  conditions,  be  made  to  appear  in 
the  spectrum  of  an  arc  light,  and  Fig.  51  shows  a  magnified 
representation  of  a  small  part  of  such  a  spectrum  adjacent 
to  the  D  (sodium)  lines.  Down  the  middle  of  each  of  these 
lines  runs  a  black  streak  whose  position  (wave  length)  is 
precisely  that  of  the  D  lines  in  the  spectrum  of  sunlight, 
and  whose  presence  is  explained  as  follows : 


146  ASTRONOMY 

The  very  hot  sodium  vapor  at  the  center  of  the  arc  gives 
off  its  characteristic  light,  which,  shining  through  the  outer 
and  cooler  layers  of  sodium  vapor,  is  partially  absorbed  by 
these,  resulting  in  a  fine  dark  line  corresponding  exactly  in 
position  and  wave  length  to  the  bright  lines,  and  seen 
against  these  as  a  background,  since  the  higher  tempera- 
ture at  the  center  of  the  arc  tends  to  broaden  the  bright 
lines  and  make  them  diffuse.  Similarly  the  dark  lines  in 
the  spectrum  of  the  sun  (Fig.  50)  point  to  the  existence  of 


D 

FIG.  51.— The  lines  reversed. 


a  surrounding  envelope  of  relatively  cool  gases,  which  absorb 
from  the  sunlight  precisely  those  kinds  of  radiant  energy 
which  they  would  themselves  emit  if  incandescent.  The 
resulting  dark  lines  in  the  spectrum  are  to  be  interpreted 
by  the  same  set  of  principles  which  we  have  above  applied 
to  the  bright  lines  of  a  discontinuous  spectrum,  and  they 
may  be  used  to  determine  the  chemical  composition  of  the 
sun,  just  as  the  bright  lines  serve  to  determine  the  chemi- 
cal elements  present  in  the  electric  arc.  With  reference  to 
the  mode  of  their  formation,  bright-line  and  dark-line  spec- 
tra are  sometimes  called  respectively  emission  and  absorp- 
tion spectra. 

88.  Types  of  spectrum, — The  sun  presents  by  far  the 
most  complex  spectrum  known,  and  Fig.  50  shows  only  a 
small  number  of  the  more  conspicuous  lines  which  appear 


INSTRUMENTS  USED  AND  PRINCIPLES  INVOLVED     147 

in  it.  Spectra  of  stars,  per  contra,  appear  relatively  simple, 
since  their  feeble  light  is  insufficient  to  bring  out  faint 
details.  In  Chapters  XIII  and  XIV  there  are  shown  types 
of  the  different  kinds  of  spectra  given  by  starlight,  and 
these  are  to  be  interpreted  by  the  principles  above  estab- 
lished. Thus  the  spectrum  of  the  bright  star  ft  Aurigse 
shows  a  continuous  spectrum  crossed  by  a  few  heavy  ab- 
sorption lines  which  are  known  from  laboratory  experi- 
ments to  be  produced  only  by  hydrogen.  There  must 
therefore  be  an  atmosphere  of  relatively  cool  hydrogen 
surrounding  this  star.  The  spectrum  of  Pollux  is  quite 
similar  to  that  of  the  sun  and  is  to  be  interpreted  as  show- 
ing a  physical  condition  similar  to  that  of  the  sun,  while 
the  spectrum  of  a  Herculis  is  quite  different  from  either  of 
the  others.  In  subsequent  chapters  we  shall  have  occasion 
to  consider  more  fully  these  different  types  of  spectrum. 

89.  The  Doppler  principle. — This  important  principle  of 
the  spectrum  analysis  is  most  readily  appreciated  through 
the  following  experiment : 

Listen  to  the  whistle  of  a  locomotive  rapidly  approach- 
ing, and  observe  how  the  pitch  changes  and  the  note  be- 
comes more  grave  as  the  locomotive  passes  by  and  com- 
mences to  recede.  During  the  approach  of  the  whistle 
each  successive  sound  wave  has  a  shorter  distance  to  travel 
in  coming  to  the  ear  of  the  listener  than  had  its  predeces- 
sor, and  in  consequence  the  waves  appear  to  come  in 
quicker  succession,  producing  a  higher  note  with  a  corre- 
spondingly shorter  wave  length  than  would  be  heard  if  the 
same  whistle  were  blown  with  the  locomotive  at  rest.  On 
the  other  hand,  the  wave  length  is  increased  and  the  pitch 
of  the  note  lowered  by  the  receding  motion  of  the  whistle. 
A  similar  effect  is  produced  upon  the  wave  length  of  light 
by  a  rapid  change  of  distance  between  the  source  from 
which  it  comes  and  the  instrument  which  receives  it,  so 
that  a  diminishing  distance  diminishes  very  slightly  the 
wave  length  of  every  line  in  the  spectrum  produced  by  the 


148  ASTRONOMY 

light,  and  an  increasing  distance  increases  these  wave 
lengths,  and  this  holds  true  whether  the  change  of  dis- 
tance is  produced  by  motion  of  the  source  of  light  or  by 
motion  of  the  instrument  which  receives  it. 

This  change  of  wave  length  is  sometimes  described  by 
saying  that  when  a  body  is  rapidly  approaching,  the  lines 
of  its  spectrum  are  all  displaced  toward  the  violet  end  of 
the  spectrum,  and  are  correspondingly  displaced  toward  the 
red  end  by  a  receding  motion.  The  amount  of  this  shift- 
ing, when  it  can  be  measured,  measures  the  velocity  of  the 
body  along  the  line  of  sight,  but  the  observations  are  ex- 
ceedingly delicate,  and  it  is  only  in  recent  years  that  it  has 
been  found  possible  to  make  them  with  precision.  For  this 
purpose  there  is  made  to  pass  through  the  spectroscope 
light  from  an  artificial  source  which  contains  one  or  more 
chemical  elements  known  to  be  present  in  the  star  which 
is  to  be  observed,  and  the  corresponding  lines  in  the 
spectrum  of  this  light  and  in  the  spectrum  of  the  star 
are  examined  to  determine  whether  they  exactly  match 
in  position,  or  show,  as  they  sometimes  do,  a  slight  dis- 
placement, as  if  one  spectrum  had  been  slipped  past 
the  other.  The  difficulty  of  the  observations  lies  in  the 
extremely  small  amount  of  this  slipping,  which  rarely  if 
ever  in  the  case  of  a  moving  star  amounts  to  one  sixth  part 
of  the  interval  between  the  close  parallel  lines  marked  D 
in  Fig.  50.  The  spectral  lines  furnished  by  the  headlight 
of  a  locomotive  running  at  the  rate  of  a  hundred  miles 
per  hour  would  be  displaced  by  this  motion  less  than  one 
six-thousandth  part  of  the  space  between  the  D  lines, 
an  amount  absolutely  imperceptible  in  the  most  powerful 
spectroscope  yet  constructed.  But  many  of  the  celestial 
bodies  have  velocities  so  much  greater  than  a  hundred 
miles  per  hour  that  these  may  be  detected  and  measured 
by  means  of  the  Doppler  principle. 

90.  Other  instruments. — Other  instruments  of  impor- 
tance to  the  astronomer,  but  of  which  only  casual  mention 


INSTRUMENTS  USED  AND  PRINCIPLES  INVOLVED    149 

can  here  be  made,  are  the  meridian-circle ;  the  transit,  one 
form  of  which  is  shown  in  Fig.  52,  and  the  zenith  tele- 
scope, which  furnish  refined  methods  for  making  observa- 
tions similar  in  kind  to  those  which  the  student  has  already 
learned  to  make  with  plumb  line  and  protractor ;  the  sex- 
tant, which  is  pre-eminently  the  sailor's  instrument  for 
finding  the  latitude  and  longitude  at  sea,  by  measuring  the 


FIG.  52. — A  combined  transit  instrument  and  zenith  telescope. 

altitudes  of  sun  and  stars  above  the  sea  horizon ;  the  heli- 
ometer,  which  serves  for  the  very  accurate  measurement  of 
small  angles,  such  as  the  angular  distance  between  two  stars 
not  more  than  one  or  two  degrees  apart ;  and  the  photom- 
eter, which  is  used  for  measuring  the  amount  of  light  re- 
ceived from  the  celestial  bodies. 


CHAPTEE  IX 

THE    MOON 

91.  Results  of  observation  with  the  unaided  eye,— The 
student  who  has  made  the  observations  of  the  moon  which 
are  indicated  in  Chapter  III  has  in  hand  data  from  which 
much  may  be  learned  about  the  earth's  satellite.  Perhaps 
the  most  striking  feature  brought  out  by  them  is  the  mo- 
tion of  the  moon  among  the  stars,  always  from  west  toward 
east,  accompanied  by  that  endless  series  of  changes  in 
shape  and  brightness — new  moon,  first  quarter,  full  moon, 
etc. — whose  successive  stages  we  represent  by  the  words, 
the  phase  of  the  moon.  From  his  own  observation  the 
student  should  be  able  to  verify,  at  least  approximately, 
the  following  statements,  although  the  degree  of  numer- 
ical precision  contained  in  some  of  them  can  be  reached 
only  by  more  elaborate  apparatus  and  longer  study  than  he 
has  given  to  the  subject : 

A.  The  phase  of  the  moon  depends  upon  the  distance 
apart   of   sun   and  moon   in  the  sky,   new   moon  coming 
when  they  are  together,  and  full  moon  when  they  are  as 
far  apart  as  possible. 

B.  The  moon  is  essentially  a  round,  dark  body,  giving 
off  no  light  of  its  own,  but  shining  solely  by  reflected  sun- 
light.    The  proof  of  this  is  that  whenever  we  see  a  part  of 
the  moon  which  is  turned  away  from  the  sun  it  looks  dark 
— e.  g.,  at  new  moon,  sun  and  moon  are  in  nearly  the  same 
direction  from  us  and  we  see  little  or  nothing  of  the  moon, 
since  the  side  upon  which  the  sun  shines  is  turned  away 
from  us.     At  full  moon  the  earth  is  in  line  between  sun 

150       • 


THE  MOON,   ONE   DAY   AFTER   FIRST  QUARTER. 

From  a  photograph  made  at  the  Paris  Observatory. 


THE  MOON  151 

and  moon,  and  we  see,  round  and  bright,  the  face  upon 
which  the  sun  shines.  At  other  phases,  such  as  the  quar- 
ters, the  moon  turns  toward  the  earth  a  part  of  its  night 
hemisphere  and  a  part  of  its  day  hemisphere,  but  in  gen- 
eral only  that  part  which  belongs  to  the  day  side  of  the 
moon  is  visible  and  the  peculiar  curved  line  which  forms 
the  boundary— the  "  ragged  edge,"  or  terminator,  as  it  is 
called,  is  the  dividing  line  between  day  and  night  upon 
the  moon. 

A  partial  exception  to  what  precedes  is  found  for  a  few 
days  after  new  moon  when  the  moon  and  sun  are  not  very 
far  apart  in  the  sky,  for  then  the  whole  round  disk  of  the 
moon  may  often  be  seen,  a  small  part  of  it  brightly  illu- 
minated by  the  sun  and  the  larger  part  feebly  illuminated 
by  sunlight  which  fell  first  upon  the  earth  and  was  by  it 
reflected  back  to  the  moon,  giving  the  pleasing  effect  which 
is  sometimes  called  the  old  moon  in  the  new  moon's  arms. 
The  new  moon — i.  e.,  the  part  illumined  by  the  sun — usu- 
ally appears  to  belong  to  a  sphere  of  larger  radius  than  the 
old  moon,  but  this  is  purely  a  trick  played  by  the  eyes  of 
the  observer,  and  the  effect  disappears  altogether  in  a  tele- 
scope. Is  there  any  similar  effect  in  the  few  days  before 
new  moon  ? 

C.  The  moon  makes  the  circuit  of  the  sky  from  a  given 
star  around  to  the  same  star  again  in  a  little  more  than 
27  days  (27.32166),  but  the  interval  between  successive  new 
moons — i.  e.,  from  the  sun  around  to  the  sun  again — is 
more  than  29  days  (29.53059).  This  last  interval,  which  is 
called  a  lunar  month  or  synodical  month,  indicates  what 
we  have  learned  before — that  the  sun  has  changed  its  place 
among  the  stars  during  the  month,  so  that  it  takes  the 
moon  an  extra  two  days  to  overtake  him  after  having 
made  the  circuit  of  the  sky,  just  as  it  takes  the  minute 
hand  of  a  clock  an  extra  5  minutes  to  catch  up  with 
the  hour  hand  after  having  made  a  complete  circuit  of  the 
dial. 


152  ASTRONOMY 

D.  Wherever  the  moon  may  be  in  the  sky,  it  turns 
always  the  same  face  toward  the  earth,  as  is  shown  by  the 
fact  that  the  dark  markings  which  appear  on  its  surface 
stand  always  upon  (nearly)  the  same  part  of  its  disk.  It 
does  not  always  turn  the  same  face  toward  the  sun,  for 
the  boundary  line  between  the  illumined  and  unillumined 
parts  of  the  moon  shifts  from  one  side  to  the  other  as  the 
phase  changes,  dividing  at  each  moment  day  from  night 
upon  the  moon  and  illustrating  by  its  slow  progress  that 
upon  the  moon  the  day  and  the  month  are  of  equal  length 
(29.5  terrestrial  days),  instead  of  being  time  units  of  differ- 
ent lengths  as  with  us. 

92.  The  moon's  motion, — The  student  should  compare  the 
results  of  his  own  observations,  as  well  as  the  preceding 
section,  with  Fig.  53,  in  which  the  lines  with  dates  printed 
on  them  are  all  supposed  to  radiate  from  the  sun  and  to 
represent  the  direction  from  the  sun  of  earth  and  moon 
upon  the  given  dates  which  are  arbitrarily  assumed  for 
the  sake  of  illustration,  any  other  set  would  do  equally 
well.  The  black  dots,  small  and  large,  represent  the 
moon  revolving  about  the  earth,  but  having  the  circular 
path  shown  in  Fig.  34  (ellipse)  transformed  by  the  earth's 
forward  motion  into  the  peculiar  sinuous  line  here  shown. 
With  respect  to  both  earth  and  sun,  the  moon's  orbit 
deviates  but  little  from  a  circle,  since  the  sinuous  curve 
of  Fig.  53  follows  very  closely  the  earth's  orbit  around 
the  sun  and  is  almost  identical  with  it.  For  clearness 
of  representation  the  distance  between  earth  and  moon 
in  the  figure  has  been  made  ten  times  too  great,  and  to 
get  a  proper  idea  of  the  moon's  orbit  with  reference  to 
the  sun,  we  must  suppose  the  moon  moved  up  toward  the 
earth  until  its  distance  from  the  line  of  the  earth's  orbit  is 
only  a  tenth  part  of  what  it  is  in  the  figure.  When  this  is 
done,  the  moon's  path  becomes  almost  indistinguishable 
from  that  of  the  earth,  as  may  be  seen  in  the  figure,  where 
the  attempt  has  been  made  to  show  both  lines,  and  it 


PIG.  53. — Motion  of  moon  and  earth  relative  to  the  sun. 
11 


154  ASTKONOMY 

is  to  be  especially  noted  that  this  real  orbit  of  the  moon  is 
everywhere  concave  toward  the  sun. 

The  phase  presented  by  the  moon  at  different  parts  of 
its  path  is  indicated  by  the  row  of  circles  at  the  right,  and 
the  student  should  show  why  a  new  moon  is  associated 
with  June  30th  and  a  full  moon  with  July  15th,  etc.  What 
was  the  date  of  first  quarter  ?  Third  quarter  ? 

We  may  find  in  Fig.  53  another  effect  of  the  same 
kind  as  that  noted  above  in  C.  Between  noon,  June  30th, 
and  noon,  July  3d,  the  earth  makes  upon  its  axis  three  com- 
plete revolutions  with  respect  to  the  sun,  but  the  meridian 
which  points  toward  the  moon  at  noon  on  June  30th  will 
not  point  toward  it  at  noon  on  July  3d,  since  the  moon  has 
moved  into  a  new  position  and  is  now  37°  away  from  the 
meridian.  Verify  this  statement  by  measuring,  in  Fig.  53, 
with  the  protractor,  the  moon's  angular  distance  from  the 
meridian  at  noon  on  July  3d.  When  will  the  meridian 
overtake  the  moon  ? 

93.  Harvest  moon. — The  interval  between  two  successive 
transits  of  the  meridian  past  the  moon  is  called  a  lunar 
day,  and  the  student  should  show  from  the  figure  that  on 
the  average  a  lunar  day  is  51  minutes  longer  than  a  solar 
day — i.  e.,  upon  the  average  each  day  the  moon  comes  to 
the  meridian  51  minutes  of  solar  time  later  than  on  the 
day  before.  It  is  also  true  that  on  the  average  the  moon 
rises  and  sets  51  minutes  later  each  day  than  on  the  day 
before.  But  there  is  a  good  deal  of  irregularity  in  the 
retardation  of  the  time  of  moonrise  and  moonset,  since 
the  time  of  rising  depends  largely  upon  the  particular 
point  of  the  horizon  at  which  the  moon  appears,  and  be- 
tween two  days  this  point  may  change  so  much  on  account 
of  the  moon's  orbital  motion  as  to  make  the  retardation 
considerably  greater  or  less  than  its  average  value.  In 
northern  latitudes  this  effect  is  particularly  marked  in  the 
month  of  September,  when  the  eastern  horizon  is  nearly 
parallel  with  the  moon's  apparent  path  in  the  sky,  and  near 


THE  MOON  155 

the  time  of  full  moon  in  that  month  the  moon  rises  on 
several  successive  nights  at  nearly  the  same  hour,  and  in 
less  degree  the  same  is  true  for  October.  This  highly 
convenient  arrangement  of  moonlight  has  caused  the  full 
moons  of  these  two  months  to  be  christened  respectively 
the  Harvest  Moon  and  the  Hunter's  Moon. 

94.  Size  and  mass  of  the  moon. — It  has  been  shown  in 
Chapter  I  how  the  distance  of  the  moon  from  the  earth 
may  be  measured  and  its  diameter  determined  by  means  of 
angles,  and  without  enlarging  upon  the  details  of  these  ob- 
servations, we  note  as  their  result  that  the  moon  is  a  globe 
2,163  miles  in  diameter,  and  distant  from  the  earth  on  the 
average  about  240,000  miles.  But,  as  we  have  seen  in 
Chapter  VII,  this  distance  changes  to  the  extent  of  a  few 
thousand  miles,  sometimes  less,  sometimes  greater,  mainly 
on  account  of  the  elliptic  shape  of  the  moon's  orbit  about 
the  earth,  but  also  in  part  from  the  disturbing  influence  of 
other  bodies,  such  as  the  sun,  which  pull  the  moon  to  and 
fro,  backward  and  forward,  to  quite  an  appreciable  extent. 

From  the  known  diameter  of  the  moon  it  is  a  matter  of 
elementary  geometry  to  derive  in  miles  the  area  of  its  sur- 
face and  its  volume  or  solid  contents.  Leaving  this  as  an 
exercise  for  the  student,  we  adopt  the  earth  as  the  standard 
of  comparison  and  find  that  the  diameter  of  the  moon  is 
rather  more  than  a  quarter,  u/g,"  that  of  the  earth,  the  area 
of  its  surface  is  a  trifle  more  than  -^  that  of  the  earth, 
and  its  volume  a  little  more  than  ¥V  of  the  earth's.  So 
much  is  pure  geometry,  but  we  may  combine  with  it  some 
mechanical  principles  which  enable  us  to  go  a  step  farther 
and  to  "  weigh  "  the  moon — i.  e.,  determine  its  mass  and 
the  average  density  of  the  material  of  which  it  is  made. 

We  have  seen  that  the  moon  moves  around  the  sun  in  a 
path  differing  but  little  from  the  smooth  curve  shown  in 
Fig.  53,  with  arrows  indicating  the  direction  of  motion, 
and  it  would  follow  absolutely  such  a  smooth  path  were 
it  not  for  the  attraction  of  the  earth,  and  in  less  degree 


156  ASTRONOMY 

of  some  of  the  other  planets,  which  swing  it  about  first 
to  one  side  then  to  the  other.  But  action  and  reaction 
are  equal  ;  the  moon  pulls  as  strongly  upon  the  earth 
as  does  the  earth  upon  the  moon,  and  if  earth  and  moon 
were  of  equal  mass,  the  deviation  of  the  earth  from  the 
smooth  curve  in  the  figure  would  be  just  as  large  as  that 
of  the  moon.  It  is  shown  in  the  figure  that  the  moon  does 
displace  the  earth  from  this  curve,  and  we  have  only  to 
measure  the  amount  of  this  displacement  of  the  earth  and 
compare  it  with  the  displacement  suffered  by  the  moon  to 
find  how  much  the  mass  of  the  one  exceeds  that  of  the 
other.  It  may  be  seen  from  the  figure  that  at  first  quarter, 
about  July  7th,  the  earth  is  thrust  ahead  in  the  direction 
of  its  orbital  motion,  while  at  the  third  quarter,  July  22d,  it 
is  pulled  back  by  the  action  of  the  moon,  and  at  all  times 
it  is  more  or  less  displaced  by  this  action,  so  that,  in  order 
to  be  strictly  correct,  we  must  amend  our  former  statement 
about  the  moon  moving  around  the  earth  and  make  it  read, 
Both  earth  and  moon  revolve  around  a  point  on  line  be- 
tween their  centers.  This  point  is  called  their  center  of 
gravity,  and  the  earth  and  the  moon  both  move  in  ellipses 
having  this  center  of  gravity  at  their  common  focus. 
Compare  this  with  Kepler's  First  Law.  These  ellipses  are 
similarly  shaped,  but  of  very  different  size,  corresponding 
to  Newton's  third  law  of  motion  (Chapter  IV),  so  that  the 
action  of  the  earth  in  causing  the  small  moon  to  move 
around  a  large  orbit  is  just  equal  to  the  reaction  of  the 
moon  in  causing  the  larger  earth  to  move  in  the  smaller 
orbit.  This  is  equivalent  to  saying  that  the  dimensions  of 
the  two  orbits  are  inversely  proportional  to  the  masses  of 
the  earth  and  the  moon. 

By  observing  throughout  the  month  the  direction  from 
the  earth  to  the  sun  or  to  a  near  planet,  such  as  Mars  or 
Venus,  astronomers  have  determined  that  the  diameter  of 
the  ellipse  in  which  the  earth  moves  is  about  5,850  miles, 
so  that  the  distance  of  the  earth  from  the  center  of  gravity 


THE  MOON  157 

is  2,925  miles,  and  the  distance  of  the  moon  from  it  is 
240,000  —  2,925  =  237,075.  We  may  now  write  in  the  form 
of  a  proportion — 

Mass  of  earth  :  Mass  of  moon  : :  237,075  :  2,925, 

and  find  from  it  that  the  mass  of  the  earth  is  81  times 
as  great  as  the  mass  of  the  moon — i.  e.,  leaving  kind  and 
quality  out  of  account,  there  is  enough  material  in  the 
earth  to  make  81  rnoons.  We  may  note  in  this  con- 
nection that  the  diameter  of  the  earth,  7,926  miles,  is 
greater  than  the  diameter  of  the  monthly  orbit  in  which 
the  moon  causes  it  to  move,  and  therefore  the  center  of 
gravity  of  earth  and  moon  always  lies  inside  the  body  of 
the  earth,  about  1,000  miles  below  the  surface. 

95.  Density  of  the  moon. — It  is  believed  that  in  a  general 
way  the  moon  is  made  of  much  the  same  kind  of  material 
which  goes  to  make  up  the  earth — metals,  minerals,  rocks, 
etc.— and  a  part  of  the  evidence  upon  which  this  belief  is 
based  lies  in  the  density  of  the  moon.  By  density  of  a 
substance  we  mean  the  amount  of  it  which  is  contained  in 
a  given  volume — i.  e.,  the  weight  of  a  bushel  or  a  cubic 
centimeter  of  the  stuff.  The  density  of  chalk  is  twice  as 
great  as  the  density  of  water,  because  a  cubic  centimeter 
of  chalk  weighs  twice  as  much  as  an  equal  volume  of 
water,  and  similarly  in  other  cases  the  density  is  found  by 
dividing  the  mass  or  weight  of  the  body  by  the  mass  or 
weight  of  an  equal  volume  of  water. 

We  know  the  mass  of  the  earth  (§  40),  and  knowing 
the  mass  of  a  cubic  foot  of  water,  it  is  easy,  although  a 
trifle  tedious,  to  compute  what  would  be  the  mass  of  a  vol- 
ume of  water  equal  in  size  to  the  earth.  The  quotient 
obtained  by  dividing  one  of  these  masses  by  the  other  (mass 
of  earth  -5-  mass  of  water)  is  the  average  density  of  the  ma- 
terial composing  the  earth,  and  we  find  numerically  that 
this  is  5.6— i.  e.,  it  would  take  5.6  water  earths  to  attract  as 
strongly  as  does  the  real  one.  From  direct  experiment  we 


158  ASTRONOMY 

know  that  the  average  density  of  the  principal  rocks  which 
make  up  the  crust  of  the  earth  is  only  about  half  of  this, 
showing  that  the  deep-lying  central  parts  of  the  earth  are 
denser  than  the  surface  parts,  as  we  should  expect  them  to 
be,  because  they  have  to  bear  the  weight  of  all  that  lies 
above  them  and  are  compressed  by  it. 

Turning  now  to  the  moon,  we  find  in  the  same  way  as 
for  the  earth  that  its  average  density  is  3.4  as  great  as  that 
of  water. 

96.  Force  of  gravity  upon  the  moon.  —  This  number,  3.4, 
compared  with  the  5.6  which  we  found  for  the  earth,  shows 
that  on  the  whole  the  moon  is  made  of  lighter  stuff  than  is 
the  body  of  the  earth,  and  this  again  is  much  what  we  should 
expect  to  find,  for  weight,  the  force  which  tends  to  com- 
press the  substance  of  the  moon,  is  less  there  than  here. 
The  weight  of  a  cubic  yard  of  rock  at  the  surface  of  either 
earth  or  moon  is  the  force  with  which  the  earth  or  moon 
attracts  it,  and  this  by  the  law  of  gravitation  is  for  the 
earth  — 

mm' 
'• 


and  for  the  moon  — 

m' 

™   si 

w  =  k.      _?L; 
(1081)2 

from  which  we  find  by  division— 

TF/3963X2 
W  =  81  - 


The  cubic  yard  of  rock,  which  upon  the  earth  weighs  two 
tons,  would,  if  transported  to  the  moon,  weigh  only  one 
third  of  a  ton,  and  would  have  only  one  sixth  as  much 
influence  in  compressing  the  rocks  below  it  as  it  had  upon 
the  earth.  Xote  that  this  rock  when  transported  to  the 
moon  would  be  still  attracted  by  the  earth  and  would  have 
weight  toward  the  earth,  but  it  is  not  this  of  which  we  are 


THE  MOON  159 

speaking ;  by  its  weight  in  the  moon  we  mean  the  force 
with  which  the  moon  attracts  it.  Making  due  allowance 
for  the  difference  in  compression  produced  by  weight,  we 
may  say  that  in  general,  so  far  as  density  goes,  the  moon  is 
very  like  a  piece  of  the  earth  of  equal  mass  set  off  by  itself 
alone. 

97.  Albedo. — In  another  respect  the  lunar  stuff  is  like 
that  of  which  the  earth  is  made  :  it  reflects  the  sunlight  in 
much  the  same  way  and  to  the  same  amount.     The  con- 
trast of  light  and  dark  areas  on  the  moon's  surface  shows, 
as  we  shall  see  in  another  section,  the  presence  of  different 
substances  upon  the  moon  which  reflect  the  sunlight  in 
different  degrees.     This  capacity  for  reflecting  a  greater  or 
less  percentage   of  the  incident   sunlight  is  called  albedo 
(Latin,  whiteness),  and  the  brilliancy  of  the  full  moon  might 
lead  one  to  suppose  that  its  albedo  is  very  great,  like  that 
of  snow  or  those  masses  of  summer  cloud  which  we  call 
thunderheads.     But  this  is  only  an  effect  of  contrast  with 
the  dark  background  of  the  sky.     The  same  moon  by  day 
looks  pale,  and  its  albedo  is,  in  fact,  not  very  different 
from  that  of  our  common  rocks — weather-beaten  sandstone 
according  to  Sir  John  Herschel — so  that  it  would  be  pos- 
sible to  build  an  artificial  moon  of   rock  or  brick  which 
would  shine  in  the  sunlight  much  as  does  the  real  moon. 

The  effect  produced  by  the  differences  of  albedo  upon 
the  moon's  face  is  commonly  called  the  "  man  in  the  moon," 
but,  like  the  images  presented  by  glowing  coals,  the  face  in 
the  moon  is  anything  which  we  choose  to  make  it.  Among 
the  Chinese  it  is  said  to  be  a  monkey  pounding  rice  ;  in 
India,  a  rabbit ;  in  Persia,  the  earth  reflected  as  in  a  mir- 
ror, etc. 

98.  Librations. — We  have  already  learned  that  the  moon 
turns  always  the  same  face  toward  the  earth,  and  we  have 
now  to  modify  this  statement  and  to  find  that  here,  as  in 
so  many  other  cases,  the  thing  we  learn  first  is  only  ap- 
proximately true  and  needs  to  be  limited  or  added  to  or 


160  ASTRONOMY 

modified  in  some  way.  In  general,  Nature  is  too  complex 
to  be  completely  understood  at  first  sight  or  to  be  per- 
fectly represented  by  a  simple  statement.  In  Fig.  55  we 
have  two  photographs  of  the  moon,  taken  nearly  three  years 
apart,  the  right-hand  one  a  little  after  first  quarter  and  the 
left-hand  one  a  little  before  third  quarter.  They  there- 
fore represent  different  parts  of  the  moon's  surface,  but 
along  the  ragged  edge  the  same  region  is  shown  on  both 
photographs,  and  features  common  to  both  pictures  may 
readily  be  found — e.  g.,  the  three  rings  which  form  a  right- 
angled  triangle  about  one  third  of  the  way  down  from  the 
top  of  the  cut,  and  the  curved  mountain  chain  just  below 
these.  If  the  moon  turned  exactly  the  same  face  toward 
us  in  the  two  pictures,  the  distance  of  any  one  of  these 
markings  from  any  part  of  the  moon's  edge  must  be  the 
same  in  both  pictures ;  but  careful  measurement  will  show 
that  this  is  not  the  case,  and  that  in  the  left-hand  pic- 
ture the  upper  edge  of  the  moon  is  tipped  toward  us  and 
the  lower  edge  away  from  us,  as  if  the  whole  moon  had 
been  rotated  slightly  about  a  horizontal  line  and  must  be 
turned  back  a  little  (about  7°)  in  order  to  match  perfectly 
the  other  part  of  the  picture. 

This  turning  is  called  a  libration,  and  it  should  be  borne 
in  mind  that  the  moon  librates  not  only  in  the  direction 
above  measured,  north  and  south,  but  also  at  right  angles 
to  this,  east  and  west,  so  that  we  are  able  to  see  a  little 
farther  around  every  part  of  the  moon's  edge  than  would 
be  possible  if  it  turned  toward  us  at  all  times  exactly  the 
same  face.  But  in  spite  of  the  librations  there  remains  on 
the  farther  side  of  the  moon  an  area  of  6,000,000  square 
miles  which  is  forever  hidden  from  us,  and  of  whose  char- 
acter we  have  no  direct  knowledge,  although  there  is  no 
reason  to  suppose  it  very  different  from  that  which  is  visi- 
ble, despite  the  fact  that  some  of  the  books  contain  quaint 
speculations  to  the  contrary.  The  continent  of  South 
America  is  just  about  equal  in  extent  to  this  unknown  re- 


THE  MOON 


161 


gion,  while  North  America  is  a  fair  equivalent  for  all  the 
rest  of  the  moon's  surface,  both  those  central  parts  which 
are  constantly  visible,  and  the  zone  around  the  edge  whose 
parts  sometimes  come  into  sight  and  are  sometimes  hidden. 

An  interesting  consequence  of  the  peculiar  rotation  of 
the  moon  is  that  from  our  side  of  it  the  earth  is  always 
visible.  Sun,  stars,  and  planets  rise  and  set  there  as  well 
as  here,  but  to  an  observer  on  the  moon  the  earth  swings 
always  overhead,  shifting  its  position  a  few  degrees  one 
way  or  the  other  on  account  of  the  libration  but  running 
through  its  succession  of  phases,  new  earth,  first  quarter, 
etc.,  without  ever  going  below  the  horizon,  provided  the 
observer  is  anywhere  near  the  center  of  the  moon's  disk. 

99.  Cause  of  librations. — That  the  moon  should  librate 
is  by  no  means  so  remarkable  a  fact  as  that  it  should  at  all 
times  turn  very  nearly  the 
same  face  toward  the  earth. 
This  latter  fact  can  have  but 
one  meaning :  the  moon  re- 
volves about  an  axis  as  does 
the  earth,  but  the  time  re- 
quired for  this  revolution  is 
just  equal  to  the  time  re- 
quired to  make  a  revolution 
in  its  orbit.  Place  two  coins 
upon  a  table  with  their  heads 
turned  toward  the  north,  as 
in  Fig.  54,  and  move  the 
smaller  one  around  the  larger 

in  such  a  way  that  its  face  shall  always  look  away  from  the 
larger  one.  In  making  one  revolution  in  its  orbit  the  head 
on  this  small  coin  will  be  successively  directed  toward  every 
point  of  the  compass,  and  when  it  returns  to  its  initial 
position  the  small  coin  will  have  made  just  one  revolu- 
tion about  an  axis  perpendicular  to  the  plane  of  its  or- 
bit. In  no  other  way  can  it  be  made  to  face  always  away 


FIG.  54. — Illustrating  the  moon's 
rotation. 


162  ASTRONOMY 

from  the  figure  at  the  center  of  its  orbit  while  moving 
around  it. 

We  are  now  in  a  position  to  understand  the  moon's 
librations,  for,  if  the  small  coin  at  any  time  moves  faster  or 
slower  in  its  orbit  than  it  turns  about  its  axis,  a  new  side 
will  be  turned  toward  the  center,  and  the  same  may  happen 
if  the  central  coin  itself  shifts  into  a  new  position.  This  is 
what  happens  to  the  moon,  for  its  orbital  motion,  like  that 
of  Mercury  (Fig.  16),  is  alternately  fast  and  slow,  and  in 
addition  to  this  there  are  present  other  minor  influences, 
such  as  the  fact  that  its  rotation  axis  is  not  exactly  per- 
pendicular to  the  plane  of  its  orbit ;  in  addition  to  this  the 
observer  upon  the  earth  is  daily  carried  by  its  rotation  from 
one  point  of  view  to  another,  etc.,  so  that  it  is  only  in  a  gen- 
eral way  that  the  rotation  upon  the  axis  and  motion  in  the 
orbit  keep  pace  with  each  other.  In  a  general  way  a  cable 
keeps  a  ship  anchored  in  the  same  place,  although  wind  and 
waves  may  cause  it  to  "  librate  "  about  the  anchor. 

How  the  moon  came  to  have  this  exact  equality  be- 
tween its  times  of  revolution  and  rotation  constitutes  a 
chapter  of  its  history  upon  which  we  shall  not  now  enter ; 
but  the  equality  having  once  been  established,  the  mechan- 
ism by  which  it  is  preserved  is  simple  enough. 

The  attraction  of  the  earth  for  the  moon  has  very 
slightly  pulled  the  latter  out  of  shape  (§  42),  so  that  the 
particular  diameter,  which  points  toward  the  earth,  is  a  lit- 
tle longer  than  any  other,  and  thus  serves  as  a  handle  which 
the  earth  lays  hold  of  and  pulls  down  into  its  lowest  possible 
position — i.  e.,  the  position  in  which  it  points  toward  the 
center  of  the  earth.  Just  how  long  this  handle  is,  remains 
unknown,  but  it  may  be  shown  from  the  law  of  gravitation 
that  less  than  a  hundred  yards  of  elongation  would  suffice 
for  the  work  it  has  to  do. 

100.  The  moon  as  a  world. — Thus  far  we  have  considered 
the  moon  as  a  satellite  of  the  earth,  dependent  upon  the 
earth,  and  interesting  chiefly  because  of  its  relation  to  it. 


THE  MOON  163 

But  the  moon  is  something  more  than  this ;  it  is  a  world  in 
itself,  very  different  from  the  earth,  although  not  wholly 
unlike  it.  The  most  characteristic  feature  of  the  earth's 
surface  is  its  division  into  land  and  water,  and 'nothing  of 
this  kind  can  be  found  upon  the  moon.  It  is  true  that  the 
first  generation  of  astronomers  who  studied  the  moon  with 
telescopes  fancied  that  the  large  dark  patches  shown  in 
Fig.  55  were  bodies  of  water,  and  named  them  oceans, 
seas,  lakes,  and  ponds,  and  to  the  present  day  we  keep 
those  names,  although  it  is  long  since  recognized  that  these 
parts  of  the  moon's  surface  are  as  dry  as  any  other.  Their 
dark  appearance  indicates  a  different  kind  of  material  from 
that  composing  the  lighter  parts  of  the  moon,  material 
with  a  different  albedo,  just  as  upon  the  earth  we  have 
light-colored  and  dark-colored  rocks,  marble  and  slate, 
which  seen  from  the  moon  must  present  similar  contrasts 
of  brightness.  Although  these  dark  patches  are  almost 
the  only  features  distinguishable  with  the  unaided  eye,  it 
is  far  otherwise  in  the  telescope  or  the  photograph,  espe- 
cially along  the  ragged  edge  where  great  numbers  of  rings 
can  be  seen,  which  are  apparently  depressions  in  the  moon 
and  are  called  craters.  These  we  find  in  great  number 
all  over  the  moon,  but,  as  the  figure  shows,  they  are  seen 
to  the  best  advantage  near  the  terminator — i.  e.,  the  divid- 
ing line  between  day  and  night,  since  the  long  shadows 
cast  here  by  the  rising  or  setting  sun  bring  out  the  details 
of  the  surface  better  than  elsewhere.  Carefully  examine 
Fig.  55  with  reference  to  these  features. 

Another  feature  which  exists  upon  both  earth  and 
moon,  although  far  less  common  there  than  here,  is  illus- 
trated in  the  chain  of  mountains  visible  near  the  termina- 
tor, a  little  above  the  center  of  the  moon  in  both  parts  of 
Fig.  55.  This  particular  range  of  mountains,  which  is 
called  the  Lunar  Apennines,  is  by  far  the  most  prominent 
one  upon  the  moon,  although  others,  the  Alps  and  Cauca- 
sus, exist.  But  for  the  most  part  the  lunar  mountains 


THE  MOON  165 

stand  alone,  each  by  itself,  instead  of  being  grouped  into 
ranges,  as  on  the  earth.  Note  in  the  figure  that  some  of 
the  lunar  mountains  stretch  out  into  the  night  side  of  the 
moon,  their  peaks  projecting  up  into  the  sunlight,  and 
thus  becoming  visible,  while  the  lowlands  are  buried  in  the 
shadow. 

A  subordinate  feature  of  the  moon's  surface  is  the  sys- 
tem of  rays  which  seem  to  radiate  like  spokes  from  some 
of  the  larger  craters,  extending  over  hill  and  valley  some- 
times for  hundreds  of  miles.  A  suggestion  of  these  rays 
may  be  seen  in  Fig.  55,  extending  from  the  great  crater 
Copernicus  a  little  southwest  of  the  end  of  the  Apennines, 
but  their  most  perfect  development  is  to  be  seen  at  the 
time  of  full  moon  around  the  crater  Tycho,  which  lies  near 
the  south  pole  of  the  moon.  Look  for  them  with  an  opera 
glass. 

Another  and  even  less  conspicuous  feature  is  furnished 
by  the  rills,  which,  under  favorable  conditions  of  illumina- 
tion, appear  like  long  cracks  on  the  moon's  surface,  per- 
haps analogous  to  the  canons  of  our  Western  country. 

101.  The  map  of  the  moon. — Fig.  55  furnishes  a  fairly 
good  map  of  a  limited  portion  of  the  moon  near  the  termi- 
nator, but  at  the  edges  little  or  no  detail  can  be  seen.  This 
is  always  true ;  the  whole  of  the  moon  can  not  be  seen  to 
advantage  at  any  one  time,  and  to  remedy  this  we  need  to 
construct  from  many  photographs  or  drawings  a  map  which 
shall  represent  the  several  parts  of  the  moon  as  they  appear 
at  their  best.  Fig.  56  shows  such  a  map  photographed  from 
a  relief  model  of  the  moon,  and  representing  the  principal 
features  of  the  lunar  surface  in  a  way  they  can  never  be 
seen  simultaneously.  Perhaps  its  most  striking  feature  is 
the  shape  of  the  craters,  which  are  shown  round  in  the  cen- 
tral parts  of  the  map  and  oval  at  the  edges,  with  their  long 
diameters  parallel  to  the  moon's  edge.  This  is,  of  course, 
an  eif ect  of  the  curvature  of  the  moon's  surface,  for  we  look 
very  obliquely  at  the  edge  portions,  and  thus  see  their  for- 


166 


ASTKONOMY 


mations  much  foreshortened  in  the  direction  of  the  moon's 
radius. 

The  north  and  south  poles  of  the  moon  are  at  the  top 
and  bottom  of  the  map  respectively,  and  a  mere  inspection 


FIG.  56.— Eelief  map  of  the  moon's  surface.— After  NASMTTH  and  CARPENTER. 

of  the  regions  around  them  will  show  how  much  more 
rugged  is  the  southern  hemisphere  of  the  moon  than  the 
northern.  It  furnishes,  too,  some  indication  of  how  numer- 
ous are  the  lunar  craters,  and  how  in  crowded  regions  they 
overlap  one  another. 

The  student  should  pick  out  upon  the  map  those  features 
which  he  has  learned  to  know  in  the  photograph  (Fig.  55) 
— the  Apennines,  Copernicus,  and  the  continuation  of  the 
Apennines,  extending  into  the  dark  part  of  the  moon. 


THE  MOON  167 

102.  Size  of  the  lunar  features. — We  may  measure  dis- 
tances here  in  the  same  way  as  upon  a  terrestrial  map,  re- 
membering that  near  the  edges  the  scale  of  the  map  is  very 
much  distorted  parallel  to  the  moon's  diameter,  and  meas- 
urements must  not  be  taken  in  this  direction,  but  may  be 
taken  parallel  to  the  edge.  Measuring  with  a  millimeter 
scale,  we  find  on  the  map  for  the  diameter  of  the  crater 
Copernicus,  2.1  millimeters.  To  turn  this  into  the  diam- 
eter of  the  real  Copernicus  in  miles,  we  measure  upon  the 
same  map  the  diameter  of  the  moon,  79.7  millimeters,  and 
then  have  the  proportion — 

Diameter  of  Copernicus  in  miles  :  2,163  : :  2.1  :  79.7, 

which  when  solved  gives  57  miles.     The  real  diameter  of 
Copernicus  is  a  trifle  over  56  miles.     At  the  eastern  edge 


FIG.  57.— Mare  Imbrium.    Photographed  at  Goodsell  Observatory. 

of  the  moon,  opposite  the  Apennines,  is  a  large  oval  spot 
called  the  Mare  Crisium  (Latin,  ma-re  =  sea).     Measure  its 


168 


ASTRONOMY 


length.  The  large  crater  to  the  northwest  of  the  Apen- 
nines is  called  Archimedes.  Measure  its  diameter  both  in 
the  map  and  in  the  photograph  (Fig.  55),  and  see  how  the 
two  results  agree.  The  true  diameter  of  this  crater,  east 
and  west,  is  very  approximately  50  miles.  The  great  smooth 
surface  to  the  west  of  Archimedes  is  the  Mare  Imbrium.  Is 

it  larger  or  smaller  than 
Lake  Superior  ?  Fig. 
57  is  from  a  photo- 
graph of  the  Mare  Im- 
brium, and  the  amount 
of  detail  here  shown  at 
the  bottom  of  the  sea 
is  a  sufficient  indica- 
tion that,  in  this  case 
at  least,  the  water  has 
been  drawn  off,  if  in- 
deed any  was  ever  pres- 
ent. 

Fig.  58  is  a  repre- 
sentation of  the  Mare 
Crisium  at  a  time  when 
night  was  beginning  to 
encroach  upon  its  east- 
ern border,  and  it 
serves  well  to  show  the 
rugged  character  of  the  ring-shaped  wall  which  incloses 
this  area. 

With  these  pictures  of  the  smoother  parts  of  the  moon's 
surface  we  may  compare  Fig.  59,  which  shows  a  region 
near  the  north  pole  of  the  moon,  and  Fig.  60,  giving  an 
early  morning  view  of  Archimedes  and  the  Apennines. 
Note  how  long  and  sharp  are  the  shadows. 

103.  The  moon's  atmosphere. — Upon  the  earth  the  sun 
casts  no  shadows  so  sharp  and  black  as  those  of  Fig.  60, 
because  his  rays  are  here  scattered  and  reflected  in  all  direc- 


FIG.  58. — Mare  Crisium. 
Lick  Observatory  photographs. 


THE  MOON 


169 


tions  by  the  dust  and  vapors  of  the  atmosphere  (§  51), 
so  that  the  place  from  which  direct  sunlight  is  cut  off 
is  at  least  partially  illumined  by  this  reflected  light.  The 
shadows  of  Fig.  60  show  that  upon  the  moon  it  must  be 
otherwise,  and  suggest  that  if  the  moon  has  any  atmosphere 
whatever,  its  density  must  be  utterly  insignificant  in  com- 
parison with  that  of  the  earth.  In  its  motion  around  the 
earth  the  moon  fre- 
quently eclipses  stars 
(occults  is  the  tech- 
nical word),  and  if  the 
moon  had  an  atmos- 
phere such  as  is  shown 
in  Fig.  61,  the  light 
from  the  star  A  must 
shine  through  this  at- 
mosphere just  before 
the  moon's  advancing 
body  cuts  it  off,  and  it 
must  be  refracted  by 
the  atmosphere  so  that 
the  star  would  appear 
in  a  slightly  different 
direction  (nearer  to 
B)  than  before.  The 
earth's  atmosphere  re- 
fracts the  starlight 

under  such  circumstances  by  more  than  a  degree,  but  no 
one  has  been  able  to  find  in  the  case  of  the  moon  any  effect 
of  this  kind  amounting  to  even  a  fraction  of  a  second  of 
arc.  While  this  hardly  justifies  the  statement  sometimes 
made  that  the  moon  has  no  atmosphere,  we  shall  be  entire- 
ly safe  in  saying  that  if  it  has  one  at  all  its  density  is  less 
than  a  thousandth  part  of  that  of  the  earth's  atmosphere. 
Quite  in  keeping  with  this  absence  of  an  atmosphere  is  the 
fact  that  clouds  never  float  over  the  surface  of  the  moon. 
12 


FIG.  59. — Illustrating  the  rugged  character  of  the 
moon's  surface. — NASMYTH  and  CARPENTER. 


170 


ASTRONOMY 


Its  features  always  stand  out  hard  and  clear,  without  any 
of  that  haze  and  softness  of  outline  which  our  atmosphere 
introduces  into  all  terrestrial  landscapes. 

104.  Height  of  the  lunar  mountains.  —  Attention  has  al- 
ready been  called  to  the  detached  mountain  peaks,  which 

in  Fig.  55  pro- 
long the  range  of 
Apennines  into 
the  lunar  night. 
These  are  the  be- 
ginnings of  the 
Caucasus  moun- 
tains, and  from 
the  photograph 
we  may  measure 
as  follows  the 
height  to  which 
they  rise  above 
the  surrounding 
level  of  the  moon  : 
Fig.  62  repre- 
sents a  part  of 

the  lunar  surface  along  the  boundary  line  between  night 
and  day,  the  horizontal  line  at  the  top  of  the  figure  repre- 
senting a  level  ray  of  sunlight  which  just  touches  the  moon 
at  T  and  barely  illuminates  the  top  of  the  mountain,  M, 
whose  height,  /i,  is  to  be  determined.  If  we  let  R  stand  for 
the  radius  of  the  moon  and  s  for  the  distance,  T  M,  we  shall 
have  in  the  right-angled  triangle  M  T  C, 


FIG.  60.— Archimedes  and  Apennines. 
NASMYTH  and  CARPENTER. 


and  we  need  only  to  measure  s  —  that  is,  the  distance  from 
the  terminator  to  the  detached  mountain  peak  —  to  make 
this  equation  determine  ^,  since  R  is  already  known,  being 
half  the  diameter  of  the  moon  —  1,081  miles.  Practically  it 
is  more  convenient  to  use  instead  of  this  equation  another 


THE  MOON 


171 


form,  which  the  student  who  is  expert  in  algebra  may  show 
to  be  very  nearly  equivalent  to  it : 

s2 
h  (miles)  =  ^-77^,  or  h  (feet)  =  2.44  s2. 


FIG.  61. — Occultations  and  the  moon's 
atmosphere. 


The  distance  s  must  be  expressed  in  miles  in  all  of  these 
equations.     In   Fig.  55  the  distance  from  the   terminator 
to  the  first  detached  peak 
of   the    Caucasus   moun- 
tains is  1.7  millimeters  = 
52  miles,  from  which  we 
find   the    height   of   the 
mountain     to     be     1.25 
miles,  or  6,600  feet. 

Two  things,  however, 
need  to  be  borne  in  mind 
in  this  connection.  On 
the  earth  we  measure  the 

heights  of  mountains  above  sea  level,  while  on  the  moon 
there  is  no  sea,  and  our  6,600  feet  is  simply  the  height  of 

the  mountain  top  above 
the  level  of  that  par- 
ticular point  in  the 
terminator,  from  which 
we  measure  its  distance. 
So  too  it  is  evident 
from  the  appearance  of 
things,  that  the  sun- 
light, instead  of  just 
touching  the  top  of  the 
particular  mountain 
whose  height  we  have 
measured,  really  extends 
some  little  distance  down  from  its  summit,  and  the  6,600 
feet  is  therefore  the  elevation  of  the  lowest  point  on  the 
mountains  to  which  the  sunlight  reaches.  The  peak  itself 


Night 


FIG.  62. — Determining  the  height  of  a  lunar 
mountain. 


172  ASTRONOMY 

may  be  several  hundred  feet  higher,  and  our  photograph 
must  be  taken  at  the  exact  moment  when  this  peak  appears 
in  the  lunar  morning  or  disappears  in  the  evening  if  we  are 
to  measure  the  altitude  of  the  mountain's  summit.  Meas- 
ure the  height  of  the  most  northern  visible  mountain  of 
the  Caucasus  range.  This  is  one  of  the  outlying  spurs  of 
the  great  mountain  Calippus,  whose  principal  peak,  19,000 
feet  high,  is  shown  in  Fig.  55  as  the  brightest  part  of  the 
Caucasus  range. 

The  highest  peak  of  the  lunar  Apennines,  Huyghens, 
has  an  altitude  of  18,000  feet,  and  the  Leibnitz  and  Doerfel 
Mountains,  near  the  south  pole  of  the  moon,  reach  an  alti- 
tude 50  per  cent  greater  than  this,  and  are  probably  the 
highest  peaks  on  the  moon.  This  falls  very  little  short  of 
the  highest  mountain  on  the  earth,  although  the  moon  is 
much  smaller  than  the  earth,  and  these  mountains  are  con- 
siderably higher  than  anything  on  the  western  continent  of 
the  earth. 

The  vagueness  of  outline  of  the  terminator  makes  it 
difficult  to  measure  from  it  with  precision,  and  somewhat 
more  accurate  determinations  of  the  heights  of  lunar 
mountains  can  be  obtained  by  measuring  the  length  of 
the  shadows  which  they  cast,  and  the  depths  of  craters 
may  also  be  measured  by  means  of  the  shadows  which  fall 
into  them. 

105.  Craters. — Fig.  63  shows  a  typical  lunar  crater,  and 
conveys  a  good  idea  of  the  ruggedness  of  the  lunar  land- 
scape. Compare  the  appearance  of  this  crater  with  the 
following  generalizations,  which  are  based  upon  the  accurate 
measurement  of  many  such  : 

A.  A  crater  is  a  real  depression  in  the  surface  of  the 
moon,  surrounded  usually  by  an  elevated  ring  which  rises 
above  the  general  level  of  the  region  outside,  while  the  bot- 
tom of  the  crater  is  about  an  equal  distance  below  that 
level. 

B.  Craters  are  shallow,  their  diameters  ranging  from 


THE  MOON  173 

five  times  to  more  than  fifty  times  their  depth.  Archi- 
medes, whose  diameter  we  found  to  be  50  miles,  has  an 
average  depth  of  about  4,000  feet  below  the  crest  of  its 
surrounding  wall,  and  is  relatively  a  shallow  crater.  . 


FIG.  63.— A  typical  lunar  crater.— NASMYTH  and  CARPENTER. 

C.  Craters   frequently  have   one   or  more   hills  rising 
within  them  which,  however,  rarely,  if  ever,  reach  up  to  the 
level  of  the  surrounding  wall. 

D.  Whatever  may  have  been  the  mode  of  their  forma- 
tion, the  craters  can  not  have  been  produced  by  scooping 
out  material  from  the  center  and  piling  it  up  to  make  the 
wall,  for  in  three  cases  out  of  four  the  volume  of  the  exca- 
vation is  greater  than  the  volume  of  material  contained  in 
the  wall. 

106.  Moon  and  earth. — We  have  gone  far  enough  now 
to  appreciate  both  the  likeness  and  the  unlikeness  of  the 
moon  and  earth.  They  may  fairly  enough  be  likened  to 
offspring  of  the  same  parent  who  have  followed  very  differ- 
ent careers,  and  in  the  fullness  of  time  find  themselves  in 
very  different  circumstances.  The  most  serious  point  of 
difference  in  these  circumstances  is  the  atmosphere,  which 
gives  to  the  earth  a  wealth  of  phenomena  altogether  lack- 


174  ASTRONOMY 

ing  in  the  moon.  Clouds,  wind,  rain,  snow,  dew,  frost,  and 
hail  are  all  dependent  upon  the  atmosphere  and  can  not  be 
found  where  it  is  not.  There  can  be  nothing  upon  the 
moon  at  all  like  that  great  group  of  changes  which  we 
call  weather,  and  the  unruffled  aspect  of  the  moon's  face 
contrasts  sharply  with  the  succession  of  cloud  and  sunshine 
which  the  earth  would  present  if  seen  from  the  moon. 

The  atmosphere  is  the  chief  agent  in  the  propagation 
of  sound,  and  without  it  the  moon  must  be  wrapped  in 
silence  more  absolute  than  can  be  found  upon  the  surface 
of  the  earth.  So,  too,  the  absence  of  an  atmosphere  shows 
that  there  can  be  no  water  or  other  liquid  upon  the  moon, 
for  if  so  it  would  immediately  evaporate  and  produce  a 
gaseous  envelope  which  we  have  seen  does  not  exist.  With 
air  and  water  absent  there  can  be  of  course  no  vegetation 
or  life  of  any  kind  upon  the  moon,  and  we  are  compelled 
to  regard  it  as  an  arid  desert,  utterly  waste. 

107.  Temperature  of  the  moon. — A  characteristic  feature 
of  terrestrial  deserts,  which  is  possessed  in  exaggerated  de- 
gree by  the  moon,  is  the  great  extremes  of  temperature  to 
which  they  and  it  are  subject.  Owing  to  its  slow  rotation 
about  its  axis,  a  point  on  the  moon  receives  the  solar  radia- 
tion uninterruptedly  for  more  than  a  fortnight,  and  that 
too  unmitigated  by  any  cloud  or  vaporous  covering.  Then 
for  a  like  period  it  is  turned  away  from  the  sun  and  allowed 
to  cool  off,  radiating  into  interplanetary  space  without  hin- 
drance its  accumulated  store  of  heat.  It  is  easy  to  see  that 
the  range  of  temperature  between  day  and  night  must  be 
much  greater  under  these  circumstances  than  it  is  with  us 
where  shorter  days  and  clouded  skies  render  day  and  night 
more  nearly  alike,  to  say  nothing  of  the  ocean  whose  waters 
serve  as  a  great  balance  wheel  for  equalizing  temperatures. 
Just  how  hot  or  how  cold  the  moon  becomes  is  hard  to 
determine,  and  very  different  estimates  are  to  be  found  in 
the  books.  Perhaps  the  most  reliable  of  these  are  fur- 
nished by  the  recent  researches  of  Professor  Very,  whose 


THE  MOON  175 

experiments  lead  him  to  conclude  that  "  its  rocky  surface  at 
midday,  in  latitudes  where  the  sun  is  high,  is  probably  hotter 
than  boiling  water  and  only  the  most  terrible  of  earth's  des- 
erts, where  the  burning  sands  blister  the  skin,  and  men, 
beasts,  and  birds  drop  dead,  can  approach  a  noontide  on 
the  cloudless  surface  of  our  satellite.  Only  the  extreme 
polar  latitudes  of  the  moon  can  have  an  endurable  tem- 
perature by  day,  to  say  nothing  of  the  night,  when  we 
should  have  to  become  troglodytes  to  preserve  ourselves 
from  such  intense  cold." 

While  the  night  temperature  of  the  moon,  even  very 
soon  after  sunset,  sinks  to  something  like  200°  below  zero 
on  the  centigrade  scale,  or  320°  below  zero  on  the  Fahren- 
heit scale,  the  lowest  known  temperature  upon  the  earth, 
according  to  General  Greely,  is  90°  Fahr.  below  zero,  re- 
corded in  Siberia  in  January,  1885. 

Winter  and  summer  are  not  markedly  different  upon 
the  moon,  since  its  rotation  axis  is  nearly  perpendicular  to 
the  plane  of  the  earth's  orbit  about  the  sun,  and  the  sun 
never  goes  far  north  or  south  of  the  moon's  equator.  The 
month  is  the  one  cycle  within  which  all  seasonal  changes  in 
its  physical  condition  appear  to  run  their  complete  course. 

108.  Changes  in  the  moon. — It  is  evidently  idle  to  look 
for  any  such  changes  in  the  condition  of  the  moon's  sur- 
face as  with  us  mark  the  progress  of  the  seasons  or 
the  spread  of  civilization  over  the  wilderness.  But  minor 
changes  there  may  be,  and  it  would  seem  that  the  violent 
oscillations  of  temperature  from  day  to  night  ought  to  have 
some  effect  in  breaking  down  and  crumbling  the  sharp 
peaks  and  crags  which  are  there  so  common  and  so  pro- 
nounced. For  a  century  past  astronomers  have  searched 
carefully  for  changes  of  this  kind — the  filling  up  of  some 
crater  or  the  fall  of  a  mountain  peak;  but  while  some 
things  of  this  kind  have  been  reported  from  time  to  time, 
the  evidence  in  their  behalf  has  not  been  altogether  conclu- 
sive. At  the  present  time  it  is  an  open  question  whether 


176 


ASTRONOMY 


changes  of  this  sort  large  enough  to  be  seen  from  the 
earth  are  in  progress.  A  crater  much  less  than  a  mile 
wide  can  be  seen  in  the  telescope,  but  it  is  not  easy  to 
tell  whether  so  minute  an  object  has  changed  in  size  or 
shape  during  a  year  or  a  decade,  and  even  if  changes  are 
seen  they  may  be  apparent  rather  than  real.  Fig.  64  con- 
tains two  views  of  the  crater  Archimedes,  taken  under  a 


f 


FIG.  64.— Archimedes  in  the  lunar  morning  and  afternoon.— WEINEK. 

morning  and  an  afternoon  sun  respectively,  and  shows  a 
very  pronounced  difference  between  the  two  which  pro- 
ceeds solely  from  a  difference  of  illumination.  In  the  pres- 
ence of  such  large  fictitious  changes  astronomers  are  slow 
to  accept  smaller  ones  as  real. 

r— '     "^  It  is  this  absence  of  change  that  is  responsible  for  the 

\     rugged  and  sharp-cut  features  of  the  moon  which  continue 

\    substantially  as  they  were  made,  while  upon  the  earth  rain 

I    and  frost  are  continually  wearing  down  the  mountains  and 

\  spreading  their  substance  upon  the  lowland  in  an  unending 

\  process  of  smoothing  off  the  roughnesses  of   its  surface. 

\  Upon  the  moon  this  process  is  almost  if  not  wholly  want- 

}  ing,  and  the  moon  abides  to-day  much  more  like  its  primi- 

;  tive  condition  than  is  the  earth. 

109.  The   moon's  influence  upon  the  earth. — There  is  a 
"widespread  popular  belief  that  in  many  ways  the  moon  exer- 


THE   MOON  177 

cises  a  considerable  influence  upon  terrestrial  affairs  :  that 
it  affects  the  weather  for  good  or  ill,  that  crops  must  be 
planted  and  harvested,  pigs  must  be  killed,  and  timber  cut 
at  the  right  time  of  the  moon,  etc.  Our  common  word 
lunatic  means  moonstruck — i.  e.,  one  upon  whom  the  moon 
has  shone  while  sleeping.  There  is  not  the  slightest  scien- 
tific basis  for  any  of  these  beliefs,  and  astronomers  every- 
where class  them  with  tales  of  witchcraft,  magic,  and  pop- 
ular delusion.  For  the  most  part  the  moon's  influence 
upon  the  earth  is  limited  to  the  light  which  it  sends  and 
the  effect  of  its  gravitation,  chiefly  exhibited  in  the  ocean 
tides.  We  receive  from  the  moon  a  very  small  amount  of 
second-hand  solar  heat  and  there  is  also  a  trifling  magnetic 
influence,  but  neither  of  these  last  effects  comes  within  the 
range  of  ordinary  observation,  and  we  shall  not  go  far  wrong 
in  saying  that,  save  the  moonlight  and  the  tides,  every  sup- 
posed lunar  influence  upon  the  earth  is  either  fictitious  or 
too  small  to  be  readily  detected. 


CHAPTEE  X 

THE   SUN 

110.  Dependence  of  the  earth  upon  the  sun. — There  is  no 
better  introduction  to  the  study  of  the  sun  than  Byron's 
Ode  to  Darkness,  beginning  with  the  lines — 

"  I  dreamed  a  dream 
That  was  not  all  a  dream. 
The  bright  sun  was  extinguished," 

and  proceeding  to  depict  in  vivid  words  the  consequences 
of  this  extinction.  The  most  matter-of-fact  language  of 
science  agrees  with  the  words  of  the  poet  in  declaring  the 
earth's  dependence  upon  the  sun  for  all  those  varied  forms 
of  energy  which  make  it  a  fit  abode  for  living  beings.  The 
winds  blow  and  the  rivers  run  ;  the  crops  grow,  are  gathered 
and  consumed,  by  virtue  of  the  solar  energy.  Factory, 
locomotive,  beast,  bird,  and  the  human  body  furnish  types 
of  machines  run  by  energy  derived  from  the  sun ;  and  the 
student  will  find  it  an  instructive  exercise  to  search  for 
kinds  of  terrestrial  energy  which  are  not  derived  either 
directly  or  indirectly  from  the  sun.  There  are  a  few  such, 
but  they  are  neither  numerous  nor  important. 

111.  The  sun's  distance  from  the  earth.— To  the  astron- 
omer the  sun  presents  problems  of  the  highest  consequence 
and  apparently  of  very  diverse  character,  but  all  tending 
toward  the  same  goal :  the  framing  of  a  mechanical  explana- 
tion of  the  sun  considered  as  a  machine,  what  it  is,  and 
how  it  does  its  work.     In  the  forefront  of  these  problems 
stand  those   numerical   determinations   of   distance,   size, 

178 


THE  SUN  179 

mass,  density,  etc.,  which  we  have  already  encountered  in 
connection  with  the  moon,  but  which  must  here  be  dealt 
with  in  a  different  manner,  because  the  immensely  greater 
distance  of  the  sun  makes  impossible  the  resort  to  any  such 
simple  method  as  the  triangle  used  for  determining  the 
moon's  distance.  It  would  be  like  determining  the  distance' 
of  a  steeple  a  mile  away  by  observing  its  'direction  first 
from  one  eye,  then  from  the  other ;  too  short  a  base  for  the 
triangle.  In  one  respect,  however,  we  stand  upon  a  better 
footing  than  in  the  case  of  the  moon,  for  the  mass  of  the 
earth  has  already  been  found  (Chapter  IV)  as  a  fractional 
part  of  the  sun's  mass,  and  we  have  only  to  invert  the 
fraction  in  order  to  find  that  the  sun's  mass  is  329,000 
times  that  of  the  earth  and  moon  combined,  or  333,000 
times  that  of  the  earth  alone. 

If  we  could  rely  implicitly  upon  this  number  we  might 
make  it  determine  for  us  the  distance  of  the  sun  through 
the  law  of  gravitation  as  follows  :  It  was  suggested  in  §  38 
that  Newton  proved  Kepler's  three  laws  to  be  imperfect 
corollaries  from  the  law  of  gravitation,  requiring  a  little 
amendment  to  make  them  strictly  correct,  and  below  we 
give  in  the  form  of  an  equation  Kepler's  statement  of  the 
Third  Law  together  with  Newton's  amendment  of  it.  In 
these  equations — 

T  =  Periodic  time  of  any  planet ; 

a  =  One  half  the  major  axis  of  its  orbit ; 

m  =  Its  mass ; 

M  =  The  mass  of  the  sun  ; 

Tc  —  The  gravitation  constant  corresponding  to  the  par- 
ticular set  of  units  in  which  J7,  #,  m,  and  M  are  expressed. 

(Kepler)  ~  =  h  ;    (Newton)  ^-=  k  (M+  m). 

Kepler's  idea  was :  For  every  planet  which  moves 
around  the  sun,  a3  divided  by  T2  always  gives  the  same 
quotient,  h  ;  and  he  did  not  concern  himself  with  the  sig- 


180  ASTRONOMY 

nificance  of  this  quotient  further  than  to  note  that  if  the 
particular  a  and  T  which  belong  to  any  planet  —  e.  g.,  the 
earth  —  be  taken  as  the  units  of  length  and  time,  then  the 
quotient  will  be  1.  Newton,  on  the  other  hand,  attached 
a  meaning  to  the  quotient,  and  showed  that  it  is  equal  to 
the  product  obtained  by  multiplying  the  sum  of  the  two 
masses,  planet  and  sun,  by  a  number  which  is  always  the 
same  when  we  are  dealing  with  the  action  of  gravitation, 
whether  it  be  between  the  sun  and  planet,  or  between 
moon  and  earth,  or  between  the  earth  and  a  roast  of  beef 
in  the  butcher's  scales,  provided  only  that  we  use  always 
the  same  units  with  which  to  measure  times,  distances, 
and  masses. 

Numerically,  Newton's  correction  to  Kepler's  Third 
Law  does  not  amount  to  much  in  the  motion  of  the 
planets.  Jupiter,  which  shows  the  greatest  effect,  makes 
the  circuit  of  his  orbit  in  4,333  days  instead  of  4,335,  which 
it  would  require  if  Kepler's  law  were  strictly  true.  But  in 
another  respect  the  change  is  of  the  utmost  importance, 
since  it  enables  us  to  extend  Kepler's  law,  which  relates 
solely  to  the  sun  and  its  planets,  to  other  attracting  bodies, 
such  as  the  earth,  moon,  and  stars.  Thus  for  the  moon's 
motion  around  the  earth  we  write  — 


from  which  we  may  find  that,  with  the  units  here  employed, 
the  earth's  mass  as  the  unit  of  mass,  the  mean  solar  day  as 
the  unit  of  time,  and  the  mile  as  the  unit  of  distance  — 

k  =  1830  X  1010. 

If  we  introduce  this  value  of  Jc  into  the  corresponding 
equation,  which  represents  the  motion  of  the  earth  around 
the  sun,  we  shall  have  — 

=  1830  X  1010  (333,000  +  1), 


(365:25)* 


THE  SUN  181 

where  the  large  number  in  the  parenthesis  represents  the 
number  of  times  the  mass  of  the  sun  is  greater  than  the 
mass  of  the  earth.  We  shall  find  by  solving  this  equation 
that  «,  the  mean  distance  of  the  sun  from  the  earth,  is 
very  approximately  93,000,000  miles. 

113.  Another  method  of  determining  the  sun's  distance,  —  N 
This  will  be  best  appreciated  by  a  reference  to  Fig.  16.  It 
appears  here  that  the  earth  makes  its  nearest  approach  to  the 
orbit  of  Mars  in  the  month  of  August,  and  if  in  any  August 
Mars  happens  to  be  in  opposition,  its  distance  from  the  earth 
will  be  very  much  less  than  the  distance  of  the  sun  from 
the  earth,  and  may  be  measured  by  methods  not  unlike 
those  which  served  for  the  moon.  If  now  the  orbits  of 
Mars  and  the  earth  were  circles  having  their  centers  at  the 
sun  this  distance  between  them,  which  we  may  represent  by 
Z>,  would  be  the  difference  of  the  radii  of  these  orbits  — 

D  =  a"  -  «',  i(ff  ' 


where  the  accents  "  '  represent  Mars  and  the  earth  respec- 
tively.    Kepler's  Third  Law  furnishes  the  relation  — 


and  since  the  periodic  times  of  the  earth  and  Mars,  T',  T", 
are  known  to  a  high  degree  of  accuracy,  these  two  equa- 
tions are  sufficient  to  determine  the  two  unknown  quanti- 
ties, 0',  a"  —  i.  e.,  the  distance  of  the  sun  from  Mars  as  well 
as  from  the  earth.  The  first  of  these  equations  is,  of 
course,  not  strictly  true,  on  account  of  the  elliptical  shape 
of  the  orbits,  but  this  can  be  allowed  for  easily  enough. 

In  practice  it  is  found  better  to  apply  this  method  of 
determining  the  sun's  distance  through  observations  of  an 
asteroid  rather  than  observations  of  Mars,  and  great  inter- 
est has  been  aroused  among  astronomers  by  the  discovery, 
in  1898,  of  an  asteroid,  or  planet,  Eros,  which  at  times  comes 
much  closer  to  the  earth  than  does  Mars  or  any  other  heav- 


182  ASTRONOMY 

enly  body  except  the  moon,  and  which  will  at  future  oppo- 
sitions furnish  a  more  accurate  determination  of  the  sun's 
distance  than  any  hitherto  available.  Observations  for  this 
purpose  are  being  made  at  the  present  time  (October,  1900). 

Many  other  methods  of  measuring  the  sun's  distance 
have  been  devised  by  astronomers,  some  of  them  extremely 
ingenious  and  interesting,  but  every  one  of  them  has  its 
weak  point — e.  g.,  the  determination  of  the  mass  of  the 
earth  in  the  first  method  given  above  and  the  measurement 
of  D  in  the  second  method,  so  that  even  the  best  results  at 
present  are  uncertain  to  the  extent  of  200,000  miles  or  more, 
and  astronomers,  instead  of  relying  upon  any  one  method, 
must  use  all  of  them,  and  take  an  average  of  their  results, 
According  to  Professor  Harkness,  this  average  value  is  92,- 
796,950  miles,  and  it  seems  certain  that  a  line  of  this  length 
drawn  from  the  earth  toward  the  sun  would  end  somewhere 
within  the  body  of  the  sun,  but  whether  on  the  nearer  or 
the  farther  side  of  the  center,  or  exactly  at  it,  no  man 
knows. 

114.  Parallax  and  distance. — It  is  quite  customary  among 
astronomers  to  speak  of  the  sun's  parallax,  instead  of  its 
distance  from  the  earth,  meaning  by  parallax  its  difference 
of  direction  as  seen  from  the  center  and  surface  of  the 
earth — i.  e.,  the  angle  subtended  at  the  sun  by  a  radius  of 
the  earth  placed  at  right  angles  to  the  line  of  sight.  The 
greater  the  sun's  distance  the  smaller  will  this  angle  be, 
and  it  therefore  makes  a  substitute  for  the  distance  which 
has  the  advantage  of  being  represented  by  a  small  number, 
8".8,  instead  of  a  large  one. 

The  books  abound  with  illustrations  intended  to  help 
the  reader  comprehend  how  great  is  a  distance  of  93,000,000 
miles,  but  a  single  one  of  these  must  suffice  here.  To  ride 
100  miles  a  day  365  days  in  the  year  would  be  counted  a 
good  bicycling  record,  but  the  rider  who  started  at  the  be- 
ginning of  the  Christian  era  and  rode  at  that  rate  toward 
the  sun  from  the  year  1  A.  D.  down  to  the  present  moment 


THE  SUN 


183 


would  not  yet  have  reached  his  destination,  although  his 
journey  would  be  about  three  quarters  done.  He  would 
have  crossed  the  orbit  of  Venus  about  the  time  of  Charle- 
magne, and  that  of 
Mercury  soon  after 
the  discovery  of 
America. 

115.  Size  and 
density  of  the  sun, 
— Knowing  the  dis- 
tance of  the  sun, 
it  is  easy  to  find 
from  the  angle  sub- 
tended by  its  di- 
ameter (32  minutes 
of  arc)  that  the 
length  of  that  di- 
ameter is  865,000 
miles.  We  recall 
in  this  connection 
that  the  diameter 
of  the  moon's  or- 
bit is  only  480,000 
miles,  but  little 
more  than  half  the 
diameter  of  the 
sun,  thus  affording 
abundant  room  in- 
side the  sun,  and 

to  spare,  for  the  moon  to  perform  the  monthly  revolution 
about  its  orbit,  as  shown  in  Fig.  65. 

In  the  same  manner  in  which  the  density  of  the  moon 
was  found  from  its  mass  and  diameter,  the  student  may 
find  from  the  mass  and  diameter  of  the  sun  given  above 
that  its  mean  density  is  1.4  times  that  of  water.  This  is 
about  the  same  as  the  density  of  gravel  or  soft  coal,  and 


FIG.  65. — The  sun's  size. — YOUNG. 


184  ASTRONOMY 

is  just  about  one  quarter  of  the  average  density  of  the 
earth. 

We  recall  that  the  small  density  of  the  moon  was  ac- 
counted for  by  the  diminished  weight  of  objects  upon  it, 
but  this  explanation  can  not  hold  in  the  case  of  the  sun, 
for  not  only  is  the  density  less  but  the  force  of  gravity 
(weight)  is  there  28  times  as  great  as  upon  the  earth.  The 
athlete  who  here  weighs  175  pounds,  if  transported  to  the 
surface  of  the  sun  would  weigh  more  than  an  elephant  does 
here,  and  would  find  his  bones  break  under  his  own  weight 
if  his  muscles  were  strong  enough  to  hold  him  upright. 
The  tremendous  pressure  exerted  by  gravity  at  the  surface 
of  the  sun  must  be  surpassed  below  the  surface,  and  as  it 
does  not  pack  the  material  together  and  make  it  dense,  we 
are  driven  to  one  of  two  conclusions  :  Either  the  stuff  of 
which  the  sun  is  made  is  altogether  unlike  that  of  the 
earth,  not  so  readily  compressed  by  pressure,  or  there  is 
some  opposing  influence  at  work  which  more  than  balances 
the  effect  of  gravity  and  makes  the  solar  stuff  much  lighter 
than  the  terrestrial. 

116.  Material  of  which  the  sun  is  made. — As  to  the  first 
of  these  alternatives,  the  spectroscope  comes  to  our  aid  and 
shows  in  the  sun's  spectrum  (Fig.  50)  the  characteristic 
line  marked  D,  which  we  know  always  indicates  the  pres- 
ence of  sodium  and  identifies  at  least  one  terrestrial  sub- 
stance as  present  in  the  sun  in  considerable  quantity.  The 
lines  marked  C  and  F  are  produced  by  hydrogen,  which  is 
one  of  the  constituents  of  water,  E  shows  calcium  to  be 
present  in  the  sun,  b  magnesium,  etc.  In  this  way  it  has 
been  shown  that  about  one  half  of  our  terrestrial  elements, 
mainly  the  metallic  ones,  are  present  as  gases  on  or  near  the 
sun's  surface,  but  it  must  not  be  inferred  that  elements  not 
found  in  this  way  are  absent  from  the  sun.  They  may  be 
there,  probably  are  there,  but  the  spectroscopic  proof  of 
their  presence  is  more  difficult  to  obtain.  Professor  Row- 
land, who  has  been  prominent  in  the  study  of  the  solar 


THE  SUN  185 

spectrum,  says  :  "  Were  the  whole  earth  heated  to  the  tem- 
perature of  the  sun,  its  spectrum  would  probably  resemble 
that  of  the  sun  very  closely." 

Some  of  the  common  terrestrial  elements  found  in  the 
sun  are  : 

Aluminium.  Nickel. 

Calcium.  Potassium. 

Carbon.  Silicon. 

Copper.  Silver. 

Hydrogen.  Sodium. 

Iron.  Tin. 

Lead.  Zinc. 
Oxygen  (?) 

Whatever  differences  of  chemical  structure  may  exist 
between  the  sun  and  the  earth,  it  seems  that  we  must  re- 
gard these  bodies  as  more  like  than  unlike  to  each  other  in 
substance,  and  we  are  brought  back  to  the  second  of  our 
alternatives  :  there  must  be  some  influence  opposing  the 
force  of  gravity  and  making  the  substance  of  the  sun  light 
instead  of  heavy,  and  we  need  not  seek  far  to  find  it  in — 

117.  The  heat  of  the  sun. — That  the  sun  is  hot  is  too 
evident  to  require  proof,  and  it  is  a  familiar  fact  that  heat 
expands  most  substances  and  makes  them  less  dense.  The 
sun's  heat  falling  upon  the  earth  expands  it  and  diminishes 
its  density  in  some  small  degree,  and  we  have  only  to  im- 
agine this  process  of  expansion  continued  until  the  earth's 
diameter  becomes  58  per  cent  larger  than  it  now  is,  to  find 
the  earth's  density  reduced  to  a  level  with  that  of  the  sun. 
Just  how  much  the  temperature  of  the  earth  must  be  raised 
to  produce  this  amount  of  expansion  we  do  not  know, 
neither  do  we  know  accurately  the  temperature  of  the  sun, 
but  there  can  be  no  doubt  that  heat  is  the  cause  of  the 
sun's  low  density  and  that  the  corresponding  temperature 
is  very  high. 

Before  we  inquire  more  closely  into  the  sun's  tempera- 
13 


186  ASTRONOMY 

ture,  it  will  be  well  to  draw  a  sharp  distinction  between  the 
two  terms  heat  and  temperature,  which  are  often  used  as  if 
they  meant  the  same  thing.  Heat  is  a  form  of  energy 
which  may  be  found  in  varying  degree  in  every  substance, 
whether  warm  or  cold — a  block  of  ice  contains  a  consider- 
able amount  of  heat — while  temperature  corresponds  to  our 
sensations  of  warm  and  cold,  and  measures  the  extent  to 
which  heat  is  concentrated  in  the  body.  It  is  the  amount 
of  heat  per  molecule  of  the  body.  A  barrel  of  warm  water 
contains  more  heat  than  the  flame  of  a  match,  but  its  tem- 
perature is  not  so  high.  Bearing  in  mind  this  distinction, 
we  seek  to  determine  not  the  amount  of  heat  contained  in 
the  sun  but  the  sun's  temperature,  and  this  involves  the 
same  difficulty  as  does  the  question,  What  is  the  tempera- 
ture of  a  locomotive  ?  It  is  one  thing  in  the  fire  box  and 
another  thing  in  the  driving  wheels,  and  still  another  at 
the  headlight ;  and  so  with  the  sun,  its  temperature  is  cer- 
tainly different  in  different  parts— one  thing  at  the  center 
and  another  at  the  surface.  Even  those  parts  which  we 
see  are  covered  by  a  veil  of  gases  which  produce  by  absorp- 
tion the  dark  lines  of  the  solar  spectrum,  and  seriously 
interfere  both  with  the  emission  of  energy  from  the  sun 
and  with  our  attempts  at  measuring  the  temperature  of 
those  parts  of  the  surface  from  which  that  energy  streams. 

In  view  of  these  and  other  difficulties  we  need  not  be 
surprised  that  the  wildest  discordance  has  been  found  in 
estimates  of  the  solar  temperature  made  by  different  investi- 
gators, who  have  assigned  to  it  values  ranging  from  1,400°  C. 
to  more  than  5,000,000°  C.  Quite  recently,  however,  im- 
proved methods  and  a  better  understanding  of  the  problem 
have  brought  about  a  better  agreement  of  results,  and  it 
now  seems  probable  that  the  temperature  of  the  visible 
surface  of  the  sun  lies  somewhere  between  5,000°  and 
10,000°  C.,  say  15,000°  of  the  Fahrenheit  scale. 

118.  Determining  the  sun's  temperature.— One  ingenious 
method  which  has  been  used  for  determining  this  tempera- 


THE  SUN  187 

ture  is  based  upon  the  principle  stated  above,  that  every 
object,  whether  warm  or  cold,  contains  heat  and  gives  it 
off  in  the  form  of  radiant  energy.  The  radiation  from  a 
body  whose  temperature  is  lower  than  500°  C.  is  made  up 
exclusively  of  energy  whose  wave  length,  is  greater  than 
7,600  tenth  meters,  and  is  therefore  invisible  to  the  eye,  al- 
though  a  thermometer  or  even  the  human  hand  can  often 
detect  it  as  radiant  heat.  A  brick  wall  in  the  summer  sun- 
shine gives  oif  energy  which  can  be  felt  as  heat  but  can 
not  be  seen.  When  such  a  body  is  further  heated  it  con- 
tinues to  send  off  the  same  kinds  (wave  lengths)  of  energy 
as  before,  but  new  and  shorter  waves  are  added  to  its  radia- 
tion, and  when  it  begins  to  emit  energy  of  wave  length  7,500 
or  7,600  tenth  meters,  it  also  begins  to  shine  with  a  dull- 
red  light,  which  presently  becomes  brighter  and  less  ruddy 
and  changes  to  white  as  the  temperature  rises,  and  waves 
of  still  shorter  length  are  thereby  added  to  the  radiation. 
We  say,  in  common  speech,  the  body  becomes  first  red  hot 
and  then  white  hot,  and  we  thus  recognize  in  a  general 
way  that  the  kind  or  color  of  the  radiation  which  a  body 
gives  off  is  an  index  to  its  temperature.  The  greater  the 
proportion  of  energy  of  short  wave  lengths  the  higher  is 
the  temperature  of  the  radiating  body.  In  sunlight  the 
maximum  of  brilliancy  to  the  eye  lies  at  or  near  the  wave 
length,  5,600  tenth  meters,  but  the  greatest  intensity  of 
radiation  of  all  kinds  (light  included)  is  estimated  to  fall 
somewhere  between  green  and  blue  in  the  spectrum  at  or 
near  the  wave  length  5,000  tenth  meters,  and  if  we  can  ap- 
ply to  this  wave  length  Paschen's  law— temperature  reck- 
oned in  degrees  centigrade  from  the  absolute  zero  is  always 
equal  to  the  quotient  obtained  by  dividing  the  number 
27,000,000  by  the  wave  length  corresponding  to  maximum 
radiation— we  shall  find  at  once  for  the  absolute  tempera- 
ture of  the  sun's  surface  5,400°  C. 

Paschen's  law  has  been  shown  to  hold  true,  at  least 
approximately,  for  lower  temperatures  and  longer  wave 


188  ASTRONOMY 

lengths  than  are  here  involved,  but  as  it  is  not  yet  certain 
that  it  is  strictly  true  and  holds  for  all  temperatures,  too 
great  reliance  must  not  be  attached  to  the  numerical  result 
furnished  by  it. 

119.  The  sun's  surface. — A  marked  contrast  exists  be- 
tween the  faces  of  sun  and  moon  in  respect  of  the  amount 


s 

FIG.  66.— The  sun,  August  11,  1894.    Photographed  at  the  Goodsell  Observatory. 

of  detail  to  be  seen  upon  them,  the  sun  showing  nothing 
whatever  to  correspond  with  the  mountains,  craters,  and 
seas  of  the  moon.  The  unaided  eye  in  general  finds  in  the 
sun  only  a  blank  bright  circle  as  smooth  and  unmarked  as 
the  surface  of  still  water,  and  even  the  telescope  at  first 
sight  seems  to  show  but  little  more.  There  may  usually  be 
found  upon  the  sun's  face  a  certain  number  of  black  patches 
called  sun  spots,  such  as  are  shown  in  Figs.  66  to  69,  and 


THE  SUN  189 

occasionally  these  are  large  enough  to  be  seen  through  a 
smoked  glass  without  the  aid  of  a  telescope.  When  seen 
near  the  edge  of  the  sun  they  are  quite  frequently  accom- 
panied, as  in  Fig.  69,  by  vague  patches  called  faculce  (Latin, 
facula  =  a  little  torch),  which  look  a  little  brighter  than 
the  surrounding  parts  of  the  sun.  So,  too,  a  good  photo- 


8 

FIG.  67.— The  sun,  August  14,  1894.    Photographed  at  the  Goodsell  Observatory. 

graph  of  the  sun  usually  shows  that  the  central  parts  of 
the  disk  are  rather  brighter  than  the  edge,  as  indeed  we 
should  expect  them  to  be,  since  the  absorption  lines  in  the 
sun's  spectrum  have  already  taught  us  that  the  visible  sur- 
face of  the  sun  is  enveloped  by  invisible  vapors  which  in 
some  measure  absorb  the  emitted  light  and  render  it  feebler 
at  the  edge  where  it  passes  through  a  greater  thickness  of 
this  envelope  than  at  the  center  (see  Fig.  70),  where  it  is 


190 


ASTRONOMY 


shown  that  the  energy  coming  from  the  edge  of  the  sun  to 
the  earth  has  to  traverse  a  much  longer  path  inside  the 
vapors  than  does  that  coming  from  the  center. 

Examine  the  sun  spots  in  the  four  photographs,  Figs. 
66  to  69,  and  note  that  the  two  spots  which  appear  at  the 
extreme  left  of  the  first  photograph,  very  much  distorted 


FIG.  68.— The  sun,  August  18,  1894.    Photographed  at  the  Goodsell  Observatory. 

and  foreshortened  by  the  curvature  of  the  sun's  surface,  are 
seen  in  a  different  part  of  the  second  picture,  and  are  not 
only  more  conspicuous  but  show  better  their  true  shape. 

120.  The  sun's  rotation. — The  changed  position  of  these 
spots  shows  that  the  sun  rotates  about  an  axis  at  right 
angles  to  the  direction  of  the  spot's  motion,  and  the  posi- 
tion of  this  axis  is  shown  in  the  figure  by  a  faint  line  ruled 
obliquely  across  the  face  of  the  sun  nearly  north  and  south 


THE  EQUA1! 


LIAL  CONSTELLATIONS 


THE  SLTN  191 

in  each  of  the  four  photographs.  This  rotation  in  the 
space  of  three  days  has  carried  the  spots  from  the  edge 
halfway  to  the  center  of  the  disk,  and  the  student  should 
note  the  progress  of  the  spots  in  the  two  later  photographs, 
that  of  August  21st  showing  them  just  ready  to  disappear 
around  the  farther  edge  of  the  sun. 


S 
FIG.  69.— The  sun,  August  21,  1894.    Photographed  at  the  Goodsell  Observatory. 

Plot  accurately  in  one  of  these  figures  the  positions  of 
the  spots  as  shown  in  the  other  three,  and  observe  whether 
the  path  of  the  spots  across  the  sun's  face  is  a  straight  line. 
Is  there  any  reason  why  it  should  not  be  straight  ? 

These  four  pictures  may  be  made  to  illustrate  many 
things  about  the  sun.  Thus  the  sun's  axis  is  not  parallel 
to  that  of  the  earth,  for  the  letters  N  S  mark  the  direction 
of  a  north  and  south  line  across  the  face  of  the  sun,  and 


192  ASTRONOMY 

this  line,  of  course,  is  parallel  to  the  earth's  axis,  while  it  is 
evidently  not  parallel  to  the  sun's  axis.      The  group  of 

spots  took  more  than 
ten  days  to  move 
across  the  sun's  face, 
and  as  at  least  an 
equal  time  must  be 
required  to  move 
around  the  opposite 
side  of  the  sun,  it  is 
evident  that  the  pe- 

FIG.  70.— Absorption  at  the  sun's  edge. 

nod  of  the  sun  s  ro- 
tation is  something  more  than  20  days.  It  is,  in  fact,  a 
little  more  than  25  days,  for  this  same  group  of  spots  reap- 
peared again  on  the  left-hand  edge  of  the  sun  on  Septem- 
ber 5th. 

121.  Sun  spots. — Another  significant  fact  comes  out 
plainly  from  the  photographs.  The  spots  are  not  perma- 
nent features  of  the  sun's  face,  since  they  changed  their 
size  and  shape  very  appreciably  in  the  few  days  covered  by 
the  pictures.  Compare  particularly  the  photographs  of 
August  14th  and  August  18th,  where  the  spots  are  least 
distorted  by  the  curvature  of  the  sun's  surface.  By  Sep- 
tember 16th  this  group  of  spots  had  disappeared  absolutely 
from  the  sun's  face,  although  when  at  its  largest  the  group 
extended  more  than  80,000  miles  in  length,  and  several  of 
the  individual  spots  were  large  enough  to  contain  the 
earth  if  it  had  been  dropped  upon  them.  From  Fig.  67 
determine  in  miles  the  length  of  the  group  on  August 
14th.  Fig.  71  shows  an  enlarged  view  of  these  spots  as 
they  appeared  on  August  17th,  and  in  this  we  find  some 
details  not  so  well  shown  in  the  preceding  pictures.  The 
larger  spots  consist  of  a  black  part  called  the  nucleus  or 
umbra  (Latin,  shadow),  which  is  surrounded  by  an  irregu- 
lar border  called  the  penumbra  (partial  shadow),  which  is 
intermediate  in  brightness  between  the  nucleus  and  the 


THE  SUN 


193 


surrounding  parts  of  the  sun.  It  should  not  be  inferred 
from  the  picture  that  the  nucleus  is  really  black  or  even 
dark.  It  shines,  in 
fact,  with  a  brilliancy 
greater  than  that  of 
an  electric  lamp,  but 
the  background  fur- 
nished by  the  sun's 
surface  is  so  much 
brighter  that  by  con- 
trast with  it  the  nu- 
cleus and  penumbra 
appear  relatively  dark. 
The  bright  shining 
surface  of  the  sun,  the 
background  for  the 
spots,  is  called  the 
photosphere  (Greek, 
light  sphere),  and,  as  Fig.  71  shows,  it  assumes  under  a 
suitable  magnifying  power  a  mottled  aspect  quite  different 


FIG.  71. — Sun  spots,  August  17,  1894. 
Goodsell  Observatory. 


FIG.  72.— Sun  spot  of  March  5,  1873.— From  LANGLKY,  The  New  Astronomy. 
By  permission  of  the  publishers. 

from  the  featureless  expanse  shown  in  the  earlier  pictures. 
The  photosphere  is,  in  fact,  a  layer  of  little  clouds  with 


194 


ASTRONOMY 


darker  spaces  between  them,  and  the  fine  detail  of  these 
clouds,  their  complicated  structure,  and  the  way  in  which, 
when  projected  against  the  background  of  a  sun  spot,  they 
produce  its  penumbra,  are  all  brought  out  in  Fig.  72. 
Note  that  the  little  patch  in  one  corner  of  this  picture 
represents  North  and  South  America  drawn  to  the  same 
scale  as  the  sun  spots. 

122.  Faculse.— We  have  seen  in  Fig.  69  a  few  of  the 
bright  spots  called  faculae.  At  the  telescope  or  in  the 
ordinary  photograph  these  can  be  seen  only  at  the  edge  of 

the  sun,  because  else- 
where the  background 
furnished  by  the  pho- 
tosphere is  so  bright 
that  they  are  lost  in  it. 
It  is  possible,  however, 
by  an  ingenious  appli- 
cation of  the  spectro- 
scope to  break  up  the 
sunlight  into  a  spec- 
trum in  such  a  way  as 
to  diminish  the  bright- 
ness of  this  back- 
ground, much  more 
than  the  brightness  of 
the  faculae  is  dimin- 
ished, and  in  this  way  to  obtain  a  photograph  of  the  sun's 
surface  which  shall  show  them  wherever  they  occur,  and 
such  a  photograph,  showing  faintly  the  spectral  lines,  is 
reproduced  in  Fig.  73.  The  faculae  are  the  bright  patches 
which  stretch  inconspicuously  across  the  face  of  the  sun, 
in  two  rather  irregular  belts  with  a  comparatively  empty 
lane  between  them.  This  lane  lies  along  the  sun's  equa- 
tor, and  it  is  upon  either  side  of  it  between  latitudes  5° 
and  40°  that  faculae  seem  to  be  produced.  It  is  significant 
of  their  connection  with  sun  spots  that  the  spots  occur 


FIG.  73. — Spectroheliograph,  showing  distribu- 
tion of  faculae  upon  the  sun. — HALE. 


196  ASTRONOMY 

in  these   particular  zones  and  are  rarely  found  outside 
them. 

123.  Invisible  parts  of  the  sun.  The  Corona. — Thus  far 
we  have  been  dealing  with  parts  of  the  sun  that  may  be 
seen  and  photographed  under  all  ordinary  conditions. 


FIG.  75.— Eclipse  of  April  16,  1893.— SCHAEBERLE. 

But  outside  of  and  surrounding  these  parts  is  an  envelope, 
or  rather  several  envelopes,  of  much  greater  extent  than 
the  visible  sun.  These  envelopes  are  for  the  most  part 
invisible  save  at  those  times  when  the  brighter  central 
portions  of  the  sun  are  hidden  in  a  total  eclipse. 

Fig.  74  is  from  a  drawing,  and  Figs.  75  and  76  are  from 
eclipse  photographs  showing  this  region,  in  which  the  most 


THE  SUN 


197 


conspicuous  object  is  the  halo  of  soft  light  called  the  corona, 
that  completely  surrounds  the  sun  but  is  seen  to  be  of  dif- 


FIG.  76.— Eclipse  of  January  21,  1898.— CAMPBELL. 


fering  shapes  and  differing  extent  at  the  several  eclipses 
here  shown,  although  a  large  part  of  these  apparent  differ- 
ences is  due  to  technical  difficulties  in  photographing,  and 
reproducing  an  object  with  outlines  so  vague  as  those  of 
the  corona.  The  outline  of  the  corona  is  so  indefinite  and 
its  outer  portions  so  faint  that  it  is  impossible  to  assign  to 
it  precise  dimensions,  but  at  its  greatest  extent  it  reaches 
out  for  several  millions  of  miles  and  fills  a  space  more  than 
twenty  times  as  large  as  the  visible  part  of  the  sun.  De- 
spite its  huge  bulk,  it  is  of  most  unsubstantial  character, 


198 


ASTRONOMY 


FIG.  77.— Solar  prominence  of  March  25, 
1895.— HALE. 


an  airy  nothing  through  which  comets  have  been  known 
to  force  their  way  around  the  sun  from  one  side  to  the 
other,  literally  for  millions  of  miles,  without  having  their 

course  influenced  or  their 
velocity  checked  to  any 
appreciable  extent.  This 
would  hardly  be  possible 
if  the  density  even  at  the 
bottom  of  the  corona  were 
greater  than  that  of  the 
best  vacuum  which  we 
are  able  to  produce  in  lab- 
oratory experiments.  It 
seems  odd  that  a  vacuum 
should  give  off  so  bright 
a  light  as  the  coronal  pic- 
tures show,  and  the  exact  character  of  that  light  and  the 
nature  of  the  corona  are  still  subjects  of  dispute  among 
astronomers,  although  it  is  generally  agreed  that,  in  part 
at  least,  its  light  is  ordinary  sunlight  faintly  reflected 
from  the  widely  scattered  molecules  composing  the  sub- 
stance of  the  corona.  It  is  also  probable  that  in  part  the 
light  has  its  origin  in  the  corona  itself.  A  curious  and  at 
present  unconfirmed  result  announced  by  one  of  the  ob- 
servers of  the  eclipse  of  May  28,  1900,  is  that  the  corona  is 
not  hot,  its  effective  temperature  being  lower  than  that  of 
the  instrument  used  for  the  observation. 

124.  The  chromosphere.— Between  the  corona  and  the 
photosphere  there  is  a  thin  separating  layer  called  the 
chromosphere  (Greek,  color  sphere),  because  when  seen  at 
an  eclipse  it  shines  with  a  brilliant  red  light  quite  unlike 
anything  else  upon  the  sun  save  the  prominences  which  are 
themselves  only  parts  of  the  chromosphere  temporarily 
thrown  above  its  surface,  as  in  a  fountain  a  jet  of  water  is 
thrown  up  from  the  basin  and  remains  for  a  few  moments 
suspended  in  mid-air.  Not  infrequently  in  such  a  foun- 


THE  SUN 


199 


tain  foreign  matter  is  swept  up  by  the  rush  of  the  water — 
dirt,  twigs,  small  fish,  etc.^-and  in  like  manner  the  promi- 
nences often  carry  along  with  them  parts  of  the  under- 
lying layers  of  the  sun,  photosphere,  faculae,  etc.,  which 
reveal  their  presence  in  the  prominence  by  adding  their 
characteristic  lines  to  the  spectrum,  like  that  of  the  chro- 
mosphere, which  the  prominence  presents  when  they  are 
absent.  None  of  the  eclipse  photographs  (Figs.  74  to  76) 
show  the  chromosphere,  because  the  color  effect  is  lacking 
in  them,  but  a  great  curving  prominence  may  be  seen  near 
the  bottom  of  Fig.  75,  and  smaller  ones  at  other  parts  of 
the  sun's  edge. 

125.  Prominences. — Fig.  77  shows  upon  a  larger  scale  one 
of  these  prominences  rising  to  a  height  of  160,000  miles 
above  the  photo- 
sphere ;  and  an- 
other photograph, 
taken  18  minutes 
later,  but  not  re- 
produced here, 
showed  the  same 
prominence  grown 
in  this  brief  inter- 
val to  a  stature 
of  280,000  miles. 
These  pictures 
were  not  taken 
during  an  eclipse, 
but  in  full  sun- 
light, using  the 
same  spectroscop- 
ic  apparatus  which 
was  employed  in 
connection  with 

the  faculae  to  diminish  the  brightness  of  the  background 
without  much  enfeebling  the  brilliancy  of  the  prominence 


FIG.  78.— A  solar  prominence.— HALE. 


200  ASTRONOMY 

itself.  The  dark  base  from  which  the  prominence  seems 
to  spring  is  not  the  sun's  edge,  but  a  part  of  the  appara- 
tus used  to  cut  off  the  direct  sunlight. 

Fig.  78  contains  a  series  of  photographs  of  another 
prominence  taken  within  an  interval  of  1  hour  47  minutes 
and  showing  changes  in  size  and  shape  which  are  much 
more  nearly  typical  of  the  ordinary  prominence  than  was 
the  very  unusual  change  in  the  case  of  Fig.  77. 

The  preceding  pictures  are  from  photographs,  and  with 
them  the  student  may  compare  Fig.  79,  which  is  con- 


FIG.  79.— Contrasted  forms  of  solar  prominences.— ZOELLNEB. 

structed  from  drawings  made  at  the  spectroscope  by  the 
German  astronomer  Zoellner.  The  changes  here  shown 
are  most  marked  in  the  prominence  at  the  left,  which  is 
shaped  like  a  broken  tree  trunk,  and  which  appears  to  be 
vibrating  from  one  side  to  the  other  like  a  reed  shaken 
in  the  wind.  Such  a  prominence  is  frequently  called  an 
eruptive  one,  a  name  suggested  by  its  appearance  of  hav- 
ing been  blown  out  from  the  sun  by  something  like  an 
explosion,  while  the  prominence  at  the  right  in  this  series 
of  drawings,  which  appears  much  less  agitated,  is  called  by 
contrast  with  the  other  a  quiescent  prominence.  These 
quiescent  prominences  are,  as  a  rule,  much  longer-lived 


THE  SUN  201 

than  the  eruptive  ones.  One  more  picture  of  prominences 
(Fig.  80)  is  introduced  to  show  the  continuous  stretch  of 
chromosphere  out  of  which  they  spring. 

Prominences  are  seen  only  at  the  edge  of  the  sun,  be- 
cause it  is  there  alone  that  the  necessary  background  can 
be  obtained,  but  they  must  occur  at  the  center  of  the  sun 
and  elsewhere  quite  as  well  as  at  the  edge,  and  it  is  prob- 
able that  quiescent  prominences  are  distributed  over  all 


FIG.  80.— Prominences  and  chromosphere.     HALE. 

parts  of  the  sun's  surface,  but  eruptive  prominences  show 
a  strong  tendency  toward  the  regions  of  sun  spots  and 
faculae  as  if  all  three  were  intimately  related  phenomena. 

126.  The  sun  as  a  machine. — Thus  far  we  have  consid- 
ered the  anatomy  of  the  sun,  dissecting  it  into  its  several 
parts,  and  our  next  step  should  be  a  consideration  of  its 
physiology,  the  relation  of  the  parts  to  each  other,  and 
their  function  in  carrying  on  the  work  of  the  solar  organ- 
ism, but  this  step,  unfortunately,  must  be  a  lame  one. 
The  science  of  astronomy  to-day  possesses  no  comprehen- 
sive and  well-established  theory  of  this  kind,  but  looks  to 
the  future  for  the  solution  of  this  the  greatest  pending 
14 


202  ASTRONOMY 

problem  of  solar  physics.  Progress  has  been  made  toward 
its  solution,  and  among  the  steps  of  this  progress  that  we 
shall  have  to  consider,  the  first  and  most  important  is  the 
conception  of  the  sun  as  a  kind  of  heat  engine. 

In  a  steam  engine  coal  is  burned  under  the  boiler,  and 
its  chemical  energy,  transformed  into  heat,  is  taken  up  by 
the  water  and  delivered,  through  steam  as  a  medium,  to 
the  engine,  which  again  transforms  and  gives  it  out  as 
mechanical  work  in  the  turning  of  shafts,  the  driving  of 
machinery,  etc.  Now,  the  function  of  the  sun  is  exactly 
opposite  to  that  of  the  engine  and  boiler  :  it  gives  out, 
instead  of  receiving,  radiant  energy ;  but,  like  the  engine, 
it  must  be  fed  from  some  source ;  it  can  not  be  run  upon 
nothing  at  all  any  more  than  the  engine  can  run  day  after 
day  without  fresh  supplies  of  fuel  under  its  boiler.  We 
know  that  for  some  thousands  of  years  the  sun  has  been 
furnishing  light  and  heat  to  the  earth  in  practically  un- 
varying amount,  and  not  to  the  earth  alone,  but  it  has 
been  pouring  forth  these  forms  of  energy  in  every  direc- 
tion, without  apparent  regard  to  either  use  or  economy. 
Of  all  the  radiant  energy  given  off  by  the  sun,  only  two 
parts  out  of  every  thousand  million  fall  upon  any  planet 
of  the  solar  system,  and  of  this  small  fraction  the  earth 
takes  about  one  tenth  for  the  maintenance  of  its  varied 
forms  of  life  and  action.  Astronomers  and  physicists  have 
sought  on  every  hand  for  an  explanation  of  the  means  by 
which  this  tremendous  output  of  energy  is  maintained 
century  after  century  without  sensible  diminution,  and 
have  come  with  almost  one  mind  to  the  conclusion  that 
the  gravitative  forces  which  reside  in  the  sun's  own  mass 
furnish  the  only  adequate  explanation  for  it,  although 
they  may  be  in  some  small  measure  re-enforced  by  minor 
influences,  such  as  the  fall  of  meteoric  dust  and  stones 
into  the  sun. 

Every  boy  who  has  inflated  a  bicycle  tire  with  a  hand 
pump  knows  that  the  pump  grows  warm  during  the  opera- 


THE  SUN  203 

tion,  on  account  of  the  compression  of  the  air  within  the 
cylinder.  A  part  of  the  muscular  force  (energy)  expended 
in  working  the  pump  reappears  in  the  heat  which  warms 
both  air  and  pump,  and  a  similar  process  is  forever  going  on 
in  the  sun,  only  in  place  of  muscular  force  we  must  there  sub- 
stitute the  tremendous  attraction  of  gravitation,  23  times 
as  great  as  upon  the  earth.  "  The  matter  in  the  interior 
of  the  sun  must  be  as  a  shuttlecock  between  the  stupen- 
dous pressure  and  the  enormously  high  temperature,"  the 
one  tending  to  compress  and  the  other  to  expand  it,  but 
with  this  important  difference  between  them :  the  tem- 
perature steadily  tends  to  fall  as  the  heat  energy  is  wasted 
away,  while  the  gravitative  force  suffers  no  corresponding 
diminution,  and  in  the  long  run  must  gain  the  upper 
hand,  causing  the  sun  to  shrink  and  become  more  dense. 
It  is  this  progressive  shrinking  and  compression  of  its 
molecules  into  a  smaller  space  which  supplies  the  energy 
contained  in  the  sun's  output  of  light  and  heat.  Accord- 
ing to  Lord  Kelvin,  each  centimeter  of  shrinkage  in  the 
sun's  diameter  furnishes  the  energy  required  to  keep  up 
its  radiation  for  something  more  than  an  hour,  and,,  on 
account  of  the  sun's  great  distance,  the  shrinkage  might 
go  on  at  this  rate  for  many  centuries  without  producing 
any  measurable  effect  in  the  sun's  appearance. 

127.  Gaseous  constitution  of  the  sun. — But  Helmholtz's  dy- 
namical theory  of  the  maintenance  of  the  sun's  heat,  which 
we  are  here  considering,  includes  one  essential  feature 
that  is  not  sufficiently  stated  above.  In  order  that  the 
explanation  may  hold  true,  it  is  necessary  that  the  sun 
should  be  in  the  main  a  gaseous  body,  composed  from  cen- 
ter to  circumference  of  gases  instead  of  solid  or  liquid 
parts.  Pumping  air  warms  the  bicycle  pump  in  a  way 
that  pumping  water  or  oil  will  not. 

The  high  temperature  of  the  sun  itself  furnishes  suffi- 
cient reason  for  supposing  the  solar  material  to  be  in  the 
gaseous  state,  but  the  gas  composing  those  parts  of  the 


204:  ASTRONOMY 

sun  below  the  photosphere  must  be  very  different  in  some 
of  its  characteristics  from  the  air  or  other  gases  with  which 
we  are  familiar  at  the  earth,  since  its  average  density  is 
1,000  times  as  great  as  that  of  air,  and  its  consistence  and 
mechanical  behavior  must  be  more  like  that  of  honey  or  tar 
than  that  of  any  gas  with  which  we  are  familiar.  It  is 
worth  noting,  however,  that  if  a  hole  were  dug  into  the 
crust  of  the  earth  to  a  depth  of  15  or  20  miles  the  air  at 
the  bottom  of  the  hole  would  be  compressed  by  that  above 
it  to  a  density  comparable  with  that  of  the  solar  gases. 

128.  The  sun's  circulation. — It  is  plain  that  under  the 
conditions  which  exist  in  the  sun  the  outer  portions,  which 
can  radiate  their  heat  freely  into  space,  must  be  cooler  than 
the  inner  central  parts,  and  this  difference  of  temperature 
must  set  up  currents  of  hot  matter  drifting  upward  and  out- 
ward from  within  the  sun  and  counter  currents  of  cooler 
matter  settling  down  to  take  its  place.  So,  too,  there  must 
be  some  level  at  which  the  free  radiation  into  outer  space 
chills  the  hot  matter  sufficiently  to  condense  its  less  refrac- 
tory gases  into  clouds  made  up  of  liquid  drops,  just  as  on  a 
cloudy  day  there  is  a  level  in  our  own  atmosphere  at  which 
the  vapor  of  water  condenses  into  liquid  drops  which  form 
the  thin  shell  of  clouds  that  hovers  above  the  earth's  surface, 
while  above  and  below  is  the  gaseous  atmosphere.  In  the 
case  of  the  sun  this  cloud  layer  is  always  present  and  is  that 
part  which  we  have  learned  to  call  the  photosphere.  Above 
the  photosphere  lies  the  chromosphere,  composed  of  gases 
less  easily  liquefied,  hydrogen  is  the  chief  one,  while  be- 
tween photosphere  and  chromosphere  is  a  thin  layer  of  me- 
tallic vapors,  perhaps  indistinguishable  from  the  top  crust 
of  the  photosphere  itself,  which  by  absorbing  the  light 
given  off  from  the  liquid  photosphere  produces  the  greater 
part  of  the  Fraunhofer  lines  in  the  solar  spectrum. 

From  time  to  time  the  hot  matter  struggling  up  from 
below  breaks  through  the  photosphere  and,  carrying  with 
it  a  certain  amount  of  the  metallic  vapors,  is  launched  into 


THE  SUN  205 

the  upper  and  cooler  regions  of  the  snn,  where,  parting 
with  its  heat,  it  falls  back  again  upon  the  photosphere  and 
is  absorbed  into  it.  It  is  altogether  probable  that  the 
corona  is  chiefly  composed  of  fine  particles  ejected  from 
the  sun  with  velocities  sufficient  to  carry  them  to  a  height 
of  millions  of  miles,  or  even  sufficient  to  carry  them  off 
never  to  return.  The  matter  of  the  corona  must  certainly 
be  in  a  state  of  the  most  lively  agitation,  its  particles  being 
alternately  hurled  up  from  the  photosphere  and  falling 
back  again  like  fireworks,  the  particles  which  make  up  the 
corona  of  to-day  being  quite  a  different  set  from  those  of 
yesterday  or  last  week.  It  seems  beyond  question  that 
the  prominences  and  faculae  too  are  produced  in  some 
way  by  this  up-and-down  circulation  of  the  sun's  matter, 
and  that  any  mechanical  explanation  of  the  sun  must  be 
worked  out  along  these  lines ;  but  the  problem  is  an  exceed- 
ingly difficult  one,  and  must  include  and  explain  many  other 
features  of  the  sun's  activity  of  which  only  a  few  can  be  con- 
sidered here. 

129.  The  sun-spot  period.— Sun  spots  come  and  go,  and 
at  best  any  particular  spot  is  but  short-lived,  rarely  lasting 
more  than  a  month  or  two,  and  more  often  its  duration  is 
a  matter  of  only  a  few  days.  They  are  not  equally  numer- 
ous at  all  times,  but,  like  swarms  of  locusts,  they  seem  to 
come  and  abound  for  a  season  and  then  almost  to  disap- 
pear, as  if  the  forces  which  produced  them  were  of  a  peri- 
odic character  alternately  active  and  quiet.  The  effect  of 
this  periodic  activity  since  1870  is  shown  in  Fig.  81,  where 
the  horizontal  line  is  a  scale  of  times,  and  the  distance  of 
the  curve  above  this  line  for  any  year  shows  the  relative 
number  of  spots  which  appeared  upon  the  sun  in  that 
year.  This  indicates  very  plainly  that  1870,  1883,  and 
1893  were  years  of  great  sun-spot  activity,  while  1879  and 
1889  were  years  in  which  few  spots  appeared.  The  older 
records,  covering  a  period  of  two  centuries,  show  the  same 
fluctuations  in  the  frequency  of  sun  spots  and  from  these 


206 


ASTRONOMY 


records  curves  (which  may  be  found  in  Young's,  The  Sun) 
have  been  plotted,  showing  a  succession  of  waves  extend- 
ing back  for  many  years. 

The  sun-spot  period  is  the  interval  of  time  from  the 
crest  or  hollow  of  one  wave  to  the  corresponding  part  of 
the  next  one,  and  on  the  average  this  appears  to  be  a  little 
more  than  eleven  years,  but  is  subject  to  considerable  varia- 
tion. In  accordance  with  this  period  there  is  drawn  in 


1870  1SSO  1890  4900  19iO 

FIG.  81. — The  curve  of  sun-spot  frequency. 

broken  lines  at  the  right  of  Fig.  81  a  predicted  continua- 
tion of  the  sun-spot  curve  for  the  first  decade  of  the  twen- 
tieth century.  The  irregularity  shown  by  the  three  pre- 
ceding waves  is  such  that  we  must  not  expect  the  actual 
course  of  future  sun  spots  to  correspond  very  closely  to 
the  prediction  here  made ;  but  in  a  general  way  1901  and 
1911  will  probably  be  years  of  few  sun  spots,  while  they 
will  be  numerous  in  1905,  but  whether  more  or  less  numer- 
ous than  at  preceding  epochs  of  greatest  frequency  can  not 
be  foretold  with  any  approach  to  certainty  so  long  as  we 
remain  in  our  present  ignorance  of  the  causes  which  make 
the  sun-spot  period. 

Determine  from  Fig.  81  as  accurately  as  possible  the 
length  of  the  sun-spot  period.  It  is  hard  to  tell  the  ex- 
act position  of  a  crest  or  hollow  of  the  curve.  Would  it 
do  to  draw  a  horizontal  line  midway  between  top  and  bot- 
tom of  the  curve  and  determine  the  length  of  the  period 


THE  SUN 


207 


from  its  intersections  with  the  curve — e.  g.,  in  1874  and 
1885? 

130.  The  sun-spot  zones. — It  has  been  already  noted  that 
sun  spots  are  found  only  in  certain  zones  of  latitude  upon 
the  sun,  and  that  faculse  and  eruptive  prominences  abound 


FIG.  82.— Illustrating  change  of  the  sun-spot  zones. 

in  these  zones  more  than  elsewhere,  although  not  strictly 
confined  to  them.  We  have  now  to  note  a  peculiarity  of 
these  zones  which  ought  to  furnish  a  clew  to  the  sun's 
mechanism,  although  up  to  the  present  time  it  has  not 
been  successfully  traced  out.  Just  before  a  sun-spot  mini- 
mum the  few  spots  which  appear  are  for  the  most  part 
clustered  near  the  sun's  equator.  As  these  spots  die  out 


208  ASTRONOMY 

two  new  groups  appear,  one  north  the  other  south  of  the 
sun's  equator  and  about  25°  or  30°  distant  from  it,  and  as 
the  period  advances  toward  a  maximum  these  groups  shift 
their  positions  more  and  more  toward  the  equator,  thus  ap- 
proaching each  other  but  leaving  between  them  a  vacant 
lane,  which  becomes  steadily  narrower  until  at  the  close 
of  the  period,  when  the  next  minimum  is  at  hand,  it 
reaches  its  narrowest  dimensions,  but  does  not  altogether 
close  up  even  then.  In  Fig.  82  these  relations  are  shown 
for  the  period  falling  between  1879  and  1890,  by  means  of 
the  horizontal  lines ;  for  each  year  one  line  in  the  north- 
ern and  one  in  the  southern  hemisphere  of  the  sun,  their 
lengths  being  proportional  to  the  number  of  spots  which 
appeared  in  the  corresponding  hemisphere  during  the  year, 
and  their  positions  on  the  sun's  disk  showing  the  average 
latitude  of  the  spots  in  question.  It  is  very  apparent  from 
the  figure  that  during  this  decade  the  sun's  southern  hemi- 
sphere was  much  more  active  than  the  northern  one  in  the 
production  of  spots,  and  this  appears  to  be  generally  the 
case,  although  the  difference  is  not  usually  as  great  as  in 
this  particular  decade. 

131.  Influence  of  the  sun-spot  period. — Sun  spots  are  cer- 
tainly less  hot  than  the  surrounding  parts  of  the  sun's  sur- 
face, and,  in  view  of  the  intimate  dependence  of  the  earth 
upon  the  solar  radiation,  it  would  be  in  no  way  surprising 
if  their  presence  or  absence  from  the  sun's  face  should 
make  itself  felt  in  some  degree  upon  the  earth,  raising  and 
lowering  its  temperature  and  quite  possibly  affecting  it  in 
other  ways.  Ingenious  men  have  suggested  many  such 
kinds  of  influence,  which,  according  to  their  investigations, 
appear  to  run  in  cycles  of  eleven  years.  Abundant  and 
scanty  harvests,  cyclones,  tornadoes,  epidemics,  rainfall, 
etc.,  are  among  these  alleged  effects,  and  it  is  possible  that 
there  may  be  a  real  connection  between  any  or  all  of  them 
and  the  sun-spot  period,  but  for  the  most  part  astronomers 
are  inclined  to  hold  that  there  is  only  one  case  in  which 


THE  SUN 

the  evidence  is  strong  enough  to  really  establish  a  connec- 
tion of  this  kind.  The  magnetic  condition  of  the  earth 
and  its  disturbances,  which  are  called  magnetic  storms,  do 
certainly  follow  in  a  very  marked  manner  the  course  of 
sun-spot  activity,  and  perhaps  there  should  be  added  to 
this  the  statement  that  auroras  (northern  lights)  stand  in 
close  relation  to  these  magnetic  disturbances  and  are  most 
frequent  at  the  times  of  sun-spot  maxima. 

Upon  the  sun,  however,  the  influence  of  the  spot  period 
is  not  limited  to  things  in  and  near  the  photosphere,  but 
extends  to  the  outermost  limits  of  the  corona.  Determine 
from  Fig.  81  the  particular  part  of  the  sun-spot  period 
corresponding  to  the  date  of  each  picture  of  the  corona 
and  note  how  the  pictures  which  were  taken  near  times  of 
sun-spot  minima  present  a  general  agreement  in  the  shape 
and  extent  of  the  corona,  while  the  pictures  taken  at  a  time 
of  maximum  activity  of  the  sun  spots  show  a  very  differ- 
ently shaped  and  much  smaller  corona. 

132.  The  law  of  the  sun's  rotation. — We  have  seen  in  a 
previous  part  of  the  chapter  how  the  time  required  by  the 
sun  to  make  a  complete  rotation  upon  its  axis  may  be  de- 
termined from  photographs  showing  the  progress  of  a  spot 
or  group  of  spots  across  its  disk,  and  we  have  now  to  add 
that  when  this  is  done  systematically  by  means  of  many 
spots  situated  in  different  solar  latitudes  it  leads  to  a 
very  peculiar  and  extraordinary  result.  Each  particular 
parallel  of  latitude  has  its  own  period  of  rotation  different 
from  that  of  its  neighbors  on  either  side,  so  that  there  can 
be  no  such  thing  as  a  fixed  geography  of  the  sun's  surface. 
Every  part  of  it  is  constantly  taking  up  a  new  position 
with  respect  to  every  other  part,  much  as  if  the  Gulf  of 
Mexico  should  be  south  of  the  United  States  this  year, 
southeast  of  it  next  year,  and  at  the  end  of  a  decade  should 
have  shifted  around  to  the  opposite  side  of  the  earth  from 
us.  A  meridian  of  longitude  drawn  down  the  Mississippi 
Valley  remains  always  a  straight  line,  or,  rather,  great 


210  ASTRONOMY 

circle,  upon  the  surface  of  the  earth,  while  Fig.  83  shows 
what  would  become  of  such  a  meridian  drawn  through 
the  equatorial  parts  of  the  sun's  disk.  In  the  first  dia- 
gram it  appears  as  a  straight  line  running  down  the  mid- 
dle of  the  sun's  disk.  Twenty-five  days  later,  when  the 
same  face  of  the  sun  comes  back  into  view  again,  after 
making  a  complete  revolution  about  the  axis,  the  equa- 
torial parts  will  have  moved  so  much  faster  and  far- 
ther than  those  in  higher  latitudes  that  the  meridian 


FIG.  83. — Effect  of  the  sun's  peculiar  rotation  in  warping  a  meridian,  originally 

straight. 

will  be  warped  as  in  the  second  diagram,  and  still  more 
warped  after  another  and  another  revolution,  as  shown  in 
the  figure. 

At  least  such  is  the  case  if  the  spots  truly  represent  the 
way  in  which  the  sun  turns  round.  There  is,  however,  a 
possibility  that  the  spots  themselves  drift  with  varying 
speeds  across  the  face  of  the  sun,  and  that  the  differences 
which  we  find  in  their  rates  of  motion  belong  to  them 
rather  than  to  the  photosphere.  Just  what  happens  in  the 
regions  near  the  poles  is  hard  to  say,  for  the  sun  spots  only 
extend  about  halfway  from  the  equator  to  the  poles,  and 
the  spectroscope,  which  may  be  made  to  furnish  a  certain 
amount  of  information  bearing  upon  the  case,  is  not  as  yet 
altogether  conclusive,  nor  are  the  faculae  which  have  also 
been  observed  for  this  purpose. 

The  simple  theory  that  the  solar  phenomena  are  caused 
by  an  interchange  of  hotter  and  cooler  matter  between  the 
photosphere  and  the  lower  strata  of  the  sun  furnishes  in 


THE  SUN  211 

its  present  shape  little  or  no  explanation  of  such  features 
as  the  sun-spot  period,  the  variations  in  the  corona,  the 
peculiar  character  of  the  sun's  rotation,  etc.,  and  we  have 
still  unsolved  in  the  mechanical  theory  of  the  sun  one  of 
the  noblest  problems  of  astronomy,  and  one  upon  which 
both  observers  and  theoretical  astronomers  are  assiduously 
working  at  the  present  time.  A  close  watch  is  kept  upon 
sun  spots  and  prominences,  the  corona  is  observed  at  every 
total  eclipse,  and  numerous  are  the  ingenious  methods 
which  are  being  suggested  and  tried  for  observing  it  with- 
out an  eclipse  in  ordinary  daylight.  Attempts,  more  or 
less  plausible,  have  been  made  and  are  now  pending  to 
explain  photosphere,  spots  and  the  reversing  layer  by  means 
of  the  refraction  of  light  within  the  sun's  outer  envelope 
of  gases,  and  it  seems  altogether  probable,  in  view  of  these 
combined  activities,  that  a  considerable  addition  to  our 
store  of  knowledge  concerning  the  sun  may  be  expected  in 
the  not  distant  future. 


CHAPTEE  XI 

THE     PLANETS 

133.  Planets. — Circling  about  the  sun,  under  the  influ- 
ence of  his  attraction,  is  a  family  of  planets  each  member 
of  which  is,  like  the  moon,  a  dark  body  shining  by  reflected 
sunlight,  and  therefore  presenting  phases ;  although  only 
two  of  them,  Mercury  and  Venus,  run  through  the  com- 
plete series — new,  first  quarter,  full,  last  quarter — which 
the  moon  presents.  The  way  in  which  their  orbits  are 
grouped  about  the  sun  has  been  considered  in  Chapter 
III,  and  Figs.  16  and  17  of  that  chapter  may  be  completed 
so  as  to  represent  all  of  the  planets  by  drawing  in  Fig.  16 
two  circles  with  radii  of  7.9  and  12.4  centimeters  respec- 
tively, to  represent  the  orbits  of  the  planets  Uranus  and 
Neptune,  which  are  more  remote  from  the  sun  than  Sat- 
urn, and  by  introducing  a  little  inside  the  orbit  of  Jupiter 
about  500  ellipses  of  different  sizes,  shapes,  and  positions  to 
represent  a  group  of  minor  planets  or  asteroids  as  they  are 
often  called.  It  is  convenient  to  regard  these  asteroids  as 
composing  by  themselves  a  class  of  very  small  planets,  while 
the  remaining  8  larger  planets  fall  naturally  into  two  other 
classes,  a  group  of  medium-sized  ones — Mercury,  Venus, 
Earth,  and  Mars — called  inner  planets  by  reason  of  their 
nearness  to  the  sun ;  and  the  outer  planets — Jupiter,  Sat- 
urn, Uranus,  Neptune — each  of  which  is  much  larger  and 
more  massive  than  any  planet  of  the  inner  group.  Com- 
pare in  Figs.  84  and  85  their  relative  sizes.  The  earth,  E,  is 
introduced  into  Fig.  85  as  a  connecting  link  between  the 
two  figures. 

Some  of  these  planets,  like  the  earth,  are  attended  by 
212 


THE  PLANETS 


213 


one  or  more  moons,  technically  called  satellites,  which  also 
shine  by  reflected  sunlight  and  which  move  about  their 
respective  planets  in  accordance  with  the  law  of  gravitation, 
much  as  the  moon  moves  around  the  earth. 


Force  of  Gravity          0.43 
Diameter         .3030 


0.88 
7700 


o.n 

2/63 


J.OO 
7927 


"Density  6.3 

Mass 


FIG.  84.  —  The  inner  planets  and  the  moon. 


134.  Distances  of  the  planets  from  the  sun. — It  is  a  com- 
paratively simple  matter  to  observe  these  planets  year  after 
year  as  they  move  among  the  stars,  and  to  find  from  these 
observations  how  long  each  one  of  them  requires  to  make 
its  circuit  around  the  sun — that  is,  its  periodic  time,  T7, 
which  figures  in  Kepler's  Third  Law,  and  when  these  peri- 
odic times  have  been  ascertained,  to  use  them  in  connection 
with  that  law  to  determine  the  mean  distance  of  each 


force  of  Gravity 
Mean  Diameter 


0.9  0.9 

32000  35000 


Density 
Mass 


i.3 

ste 


FIG.  85.— The  outer  planets. 

planet  from  the  sun.  Thus,  Jupiter  requires  4,333  days  to 
move  completely  around  its  orbit ;  and  comparing  this  with 
the  periodic  time  and  mean  distance  of  the  earth  we  find— 

fl3        _  (93?000,000)3; 
(4333)2  ~      (365.S5)2 


214  ASTRONOMY 

which  when  solved  gives  as  the  mean  distance  of  Jupiter 
from  the  sun,  483,730,000  miles,  or  5.20  times  as  distant  as 
the  earth.  If  we  make  a  similar  computation  for  each 
planet,  we  shall  find  that  their  distances  from  the  sun  show 
a  remarkable  agreement  with  an  artificial  series  of  numbers 
called  Bode's  law.  We  write  down  the  numbers  contained 
in  the  first  line  of  figures  below,  each  of  which,  after  the 
second,  is  obtained  by  doubling  the  preceding  one,  add  4 
to  each  number  and  point  off  one  place  of  decimals;  the 
resulting  number  is  (approximately)  the  distance  of  the 
corresponding  planet  from  the  sun. 


1 

3 

a 
1 

@ 

1 

3 

j& 
'3. 

3 

3 

d 

I 

0 

3 

6 

12 

24 

48 

96 

192 

384 

4 

4 

4 

4 

4 

4 

4 

4 

4 

0.4 

0.7 

1.0 

1.6 

2.8 

5.2 

10.0 

19.6 

38.8 

0.4 

0.7 

1.0 

1.5 

2.8 

5.2 

9.5 

19.2 

30.1 

The  last  line  of  figures  shows  the  real  distance  of  the 
planet  as  determined  from  Kepler's  law,  the  earth's  mean 
distance  from  the  sun  being  taken  as  the  unit  for  this  pur- 
pose. With  exception  of  Neptune,  the  agreement  between 
Bode's  law  and  the  true  distances  is  very  striking,  but  most 
remarkable  is  the  presence  in  the  series  of  a  number,  2.8, 
with  no  planet  corresponding  to  it.  This  led  astronomers 
at  the  time  Bode  published  the  law,  something  more  than 
a  century  ago,  to  give  new  heed  to  a  suggestion  made  long 
before  by  Kepler,  that  there  might  be  an  unknown  planet 
moving  between  the  orbits  of  Mars  and  Jupiter,  and  a  num- 
ber of  them  agreed  to  search  for  such  a  planet,  each  in  a 
part  of  the  sky  assigned  him  for  that  purpose.  But  they 
were  anticipated  by  Piazzi,  an  Italian,  who  found  the  new 
planet,  by  accident,  on  the  first  day  of  the  nineteenth  cen- 
tury, moving  at  a  distance  from  the  sun  represented  by  the 
number  2.77. 


THE  PLANETS  215 

This  planet  was  the  first  of  the  asteroids,  and  in  the 
century  that  has  elapsed  hundreds  of  them  have  been  dis- 
covered, while  at  the  present  time  no  year  passes  by  with- 
out several  more  being  added  to  the  number.  While  some 
of  these  are  nearer  to  the  sun  than  is  the  first  one  discov? 
ered,  and  others  are  farther  from  it,  their  average  distance 
is  fairly  represented  by  the  number  2.8. 

Why  Bode's  law  should  hold  true,  or  even  so  nearly 
true  as  it  does,  is  an  unexplained  riddle,  and  many  astron- 
omers are  inclined  to  call  it  no  law  at  all,  but  only  a  chance 
coincidence— an  illustration  of  the  "  inherent  capacity  of 
figures  to  be  juggled  with  " ;  but  if  so,  it  is  passing  strange 
that  it  should  represent  the  distance  of  the  asteroids  and 
of  Uranus,  which  was  also  an  undiscovered  planet  at  the 
time  the  law  was  published. 

135.  The  planets  compared  with  each  other. — When  we 
pass  from  general  considerations  to  a  study  of  the  indi- 
vidual peculiarities  of  the  planets,  we  find  great  differences 
in  the  extent  of  knowledge  concerning  them,  and  the  reason 
for  this  is  not  far  to  seek.  Neptune  and  Uranus,  at  the 
outskirts  of  the  solar  system,  are  so  remote  from  us  and  so 
feebly  illumined  by  the  sun  that  any  detailed  study  of  them 
can  go  but  little  beyond  determining  the  numbers  which 
represent  their  size,  mass,  density,  the  character  of  their 
orbits,  etc.  The  asteroids  are  so  small  that  in  the  telescope 
they  look  like  mere  points  of  light,  absolutely  indistinguish- 
able in  appearance  from  the  fainter  stars.  Mercury,  al- 
though closer  at  hand  and  presenting  a  disk  of  considerable 
size,  always  stands  so  near  the  sun  that  its  observation  is 
difficult  on  this  account.  Something  of  the  same  kind  is 
true  for  Venus,  although  in  much  less  degree  ;  while  Mars, 
Jupiter,  and  Saturn  are  comparatively  easy  objects  for  tele- 
scopic study,  and  our  knowledge  of  them,  while  far  from 
complete,  is  considerably  greater  than  for  the  other  planets. 

Figs.  84  and  85  show  the  relative  sizes  of  the  planets 
composing  the  inner  and  outer  groups  respectively,  and  fur- 


216  ASTRONOMY 

nish  the  numerical  data  concerning  their  diameters,  masses, 
densities,  etc.,  which  are  of  most  importance  in  judging  of 
their  physical  condition.  Each  planet,  save  Saturn,  is 
represented  by  two  circles,  of  which  the  outer  is  drawn 
proportional  to  the  size  of  the  planet,  and  the  inner  shows 
the  amount  of  material  that  must  be  subtracted  from  the 
interior  in  order  that  the  remaining  shell  shall  just  float  in 
water.  Note  the  great  difference  in  thickness  of  shell 
between  the  two  groups.  Saturn,  having  a  mean  density 
less  than  that  of  water,  must  have  something  loaded  upon 
it,  instead  of  removed,  in  order  that  it  should  float  just 
submerged. 

JUPITER 

136.  Appearance, — Commencing  our  consideration  of  the 
individual  planets  with  Jupiter,  which  is  by  far  the  largest 
of  them,  exceeding  both  in  bulk  and  mass  all  the  others 
combined,   we   have   in   Fig.   86   four    representations    of 
Jupiter  and  his  family  of  satellites  as  they  may  be  seen  in 
a  very  small  telescope — e.  g.,  an  opera  glass — save  that  the 
little  dots  which  here  represent  the  satellites  are  numbered 
j?,  #,  $,  4->  in  order  to  preserve  their  identity  in  the  succes- 
sive pictures. 

The  chief  interest  of  these  pictures  lies  in  the  satellites, 
but,  reserving  them  for  future  consideration,  we  note  that 
the  planet  itself  resembles  in  shape  the  full  moon,  although 
in  respect  of  brightness  it  sends  to  us  less  than  ^Vo  Par^ 
as  much  light  as  the  moon.  From  a  consideration  of  the 
motion  of  Jupiter  and  the  earth  in  Fig.  16,  show  that 
Jupiter  can  not  present  any  such  phases  as  does  the  moon, 
but  that  its  disk  must  be  at  all  times  nearly  full.  As  seen 
from  Saturn,  what  kind  of  phases  would  Jupiter  present  ? 

137.  The  belts. — Even  upon  the  small  scale  of  Fig.  86 
we  detect  the  most  characteristic  feature  of  Jupiter's  ap- 
pearance in  the  telescope,  the  two  bands  extending  across 
his  face  parallel  to  the  line  of  the  satellites,  and  in  Fig.  87 
these  same  dark  bands  may  be  recognized  amid  the  abun- 


THE  PLANETS  217 

dance  of  detail  which  is  here  brought  out  by  a  large  tele- 
scope. Photography  does  not  succeed  as  a  means  of  repro- 
ducing this  detail,  and  for  it  we  have  to  rely  upon  the  skill 
of  the  artist  astronomer.  The  lettering  shows  the  Pacific 


FIG.  86. — Jupiter  and  his  satellites. 

Standard  time  at  which  the  sketches  were  made,  and  also 
the  longitude  of  the  meridian  of  Jupiter  passing  down  the 
center  of  the  planet's  disk. 

The  dark  bands  are  called  technically  the  belts  of  Jupi- 
ter ;  and  a  comparison  of  these  belts  in  the  second  and  third 
pictures  of  the  group,  in  which  nearly  the  same  face  of  the 
planet  is  turned  toward  us,  will  show  that  they  are  subject 
to  considerable  changes  of  form  and  position  even  within 
the  space  of  a  few  days.  So,  too,  by  a  comparison  of  such 
markings  as  the  round  white  spots  in  the  upper  parts  of 
the  disks,  and  the  indentations  in  the  edges  of  the  belts, 
we  may  recognize  that  the  planet  is  in  the  act  of  turning 
round,  and  must  therefore  have  an  axis  about  which  it 
turns,  and  poles,  an  equator,  etc.  The  belts  are  in  fact 
parallel  to  the  planet's  equator  ;  and  generalizing  from  what 
appears  in  the  pictures,  we  may  say  that  there  is  always  a 
strongly  marked  belt  on  each  side  of  the  equator  with  a 
15 


FIG.  87.— Drawings  of  Jupiter  made  at  the  36-inch  telescope  of  the  Lick 
Observatory. — KEELER. 


THE  PLANETS  219 

lighter  colored  streak  between  them,  and  that  farther  from 
the  equator  are  other  belts  variable  in  number,  less  con- 
spicuous, and  less  permanent  than  the  two  first  seen.  Com- 
pare the  position  of  the  principal  belts  with  the  position  of 
the  zones  of  sun-spot  activity  in  the  sun.  A  feature  of 
the  planet's  surface,  which  can  not  be  here  reproduced,  is 
the  rich  color  effect  to  be  found  upon  it.  The  principal 
belts  are  a  brick-red  or  salmon  color,  the  intervening  spaces 
in  general  white  but  richly  mottled,  and  streaked  with 
purples,  browns,  and  greens. 

The  drawings  show  the  planet  as  it  appeared  in  the 
telescope,  inverted,  and  they  must  be  turned  upside  down 
if  we  wish  the  points  of  the  compass  to  appear  as  upon  a 
terrestrial  map.  Bearing  this  in  mind,  note  in  the  last 
picture  the  great  oval  spot  in  the  southern  hemisphere  of 
Jupiter.  This  is  a  famous  marking,  known  from  its  color 
as  the  great  red  spot,  which  appeared  first  in  1878  and  has 
persisted  to  the  present  day  (1900),  sometimes  the  most 
conspicuous  marking  on  the  planet,  at  others  reduced  to  a 
mere  ghost  of  itself,  almost  invisible  save  for  the  inden- 
tation which  it  makes  in  the  southern  edge  of  the  belt 
near  it. 

138.  Rotation  and  flattening  at  the  poles, — One  further 
significant  fact  with  respect  to  Jupiter  may  be  obtained 
from  a  careful  measurement  of  the  drawings  ;  the  planet  is 
flattened  at  the  poles,  so  that  its  polar  diameter  is  about 
one  sixteenth  part  shorter  than  the  equatorial  diameter. 
The  flattening  of  the  earth  amounts  to  only  one  three- 
hundredth  part,  and  the  marked  difference  between  these 
two  numbers  finds  its  explanation  in  the  greater  swiftness 
of  Jupiter's  rotation  about  its  axis,  since  in  both  cases  it  is 
this  rotation  which  makes  the  flattening. 

It  is  not  easy  to  determine  the  precise  dimensions  of  the 
planet,  since  this  involves  a  knowledge  both  of  its  distance 
from  us  and  of  the  angle  subtended  by  its  diameter,  but 
the  most  recent  determinations  of  this  kind  assign  as  the 


220  ASTRONOMY 

equatorial  diameter  90,200  miles,  and  for  the  polar  diam- 
eter 84,400  miles.  Determine  from  either  of  these  num- 
bers the  size  of  the  great  red  spot. 

The  earth  turns  on  its  axis  once  in  24  hours  but  no 
such  definite  time  can  be  assigned  to  Jupiter,  which,  like 
the  sun,  seems  to  have  different  rotation  periods  in  differ- 
ent latitudes — 9h.  50m.  in  the  equatorial  belt  and  9h.  56m. 
in  the  dark  belts  and  higher  latitudes.  There  is  some  indi- 
cation that  the  larger  part  of  the  visible  surface  rotates  in 
9h.  55.6m.,  while  a  broad  stream  along  the  equator  flows 
eastward  some  270  miles  per  hour,  and  thus  comes  back  to 
the  center  of  the  planet,  as  seen  from  the  earth,  five  or  six 
minutes  earlier  than  the  parts  which  do  not  share  in  this 
motion.  Judged  by  terrestrial  standards,  270  miles  per 
hour  is  a  great  velocity,  but  Jupiter  is  constructed  on  a 
colossal  scale,  and,  too,  we  have  to  compare  this  movement, 
not  to  a  current  flowing  in  the  ocean,  but  to  a  wind  blow- 
ing in  the  upper  regions  of  the  earth's  atmosphere.  The 
visible  surface  of  Jupiter  is  only  the  top  of  a  cloud  forma- 
tion, and  contains  nothing  solid  or  permanent,  if  indeed 
there  is  anything  solid  even  at  the  core  of  the  planet.  The 
great  red  spot  during  the  first  dozen  years  of  its  existence, 
instead  of  remaining  fixed  relative  to  the  surrounding  for- 
mations, drifted  two  thirds  of  the  way  around  the  planet, 
and  having  come  to  a  standstill  about  1891,  it  is  now  slowly 
retracing  its  path. 

139.  Physical  condition. — For  a  better  understanding  of 
the  physical  condition  of  Jupiter,  we  have  now  to  consider 
some  independent  lines  of  evidence  which  agree  in  point- 
ing to  the  conclusion  that  Jupiter,  although  classed  with 
the  earth  as  a  planet,  is  in  its  essential  character  much 
more  like  the  sun. 

Appearance. — The  formations  which  we  see  in  Fig.  87 
look  like  clouds.  They  gather  and  disappear,  and  the  only 
element  of  permanence  about  them  is  their  tendency  to 
group  themselves  along  zones  of  latitude.  If  we  measure 


THE   PLANETS  221 

the  light  reflected  from  the  planet  we  find  that  its  albedo 
is  very  high,  like  that  of  snow  or  our  own  cumulus  clouds, 
and  it  is  of  course  greater  from  the  light  parts  of  the  disk 
than  from  the  darker  bands.  The  spectroscope  shows  that 
the  sunlight  reflected  from  these  darker  belts  is  like  that 
reflected  from  the  lighter  parts,  save  that  a  larger  portion  of 
the  blue  and  violet  rays  has  been  absorbed  out  of  it,  thus 
producing  the  ruddy  tint  of  the  belts,  as  sunset  colors  are 
produced  on  the  earth,  and  showing  that  here  the  light  has 
penetrated  farther  into  the  planet's  atmosphere  before 
being  thrown  back  by  reflection  from  lower-lying  cloud  sur- 
faces. The  dark  bands  are  therefore  to  be  regarded  as  rifts 
in  the  clouds,  reaching  down  to  some  considerable  distance 
and  indicating  an  atmosphere  of  great  depth.  The  great 
red  spot,  28,000  miles  long,  and  obviously  thrusting  back 
the  white  clouds  on  every  side  of  it,  year  after  year,  can 
hardly  be  a  mere  patch  on  the  face  of  the  planet,  but  indi- 
cate? aome  considerable  depth  of  atmosphere. 

Density. — So,  too,  the  small  mean  density  of  the  planet, 
only  1.3  times  that  of  water  and  actually  less  than  the  den- 
sity of  the  sun,  suggests  that  the  larger  part  of  the  planet's 
bulk  may  be  made  of  gases  and  clouds,  with  very  little  solid 
matter  even  at  the  center ;  but  here  we  get  into  a  difficulty 
from  which  there  seems  but  one  escape.  The  force  of 
gravity  at  the  visible  surface  of  Jupiter  may  be  found 
from  its  mass  and  dimensions  to  be  2.6  times  as  great  as 
at  the  surface  of  the  earth,  and  the  pressure  exerted  upon 
iis  atmosphere  by  this  force  ought  to  compress  the  lower 
strata  into  something  more  dense  than  we  find  in  the 
)lanet.  Some  idea  of  this  compression  may  be  obtained 
from  Fig.  88,  where  the  line  marked  E  shows  approximately 
low  the  density  of  the  air  increases  as  we  move  from  its 
ipper  strata  down  toward  the  surface  of  the  earth  through 
distance  of  16  miles,  the  density  at  any  level  being  pro- 
>rtional  to  the  distance  of  the  curved  line  from  the  straight 
oiae  near  it.  The  line  marked  J  in  the  same  figure  shows 


222  ASTRONOMY 

how  the  density  would  increase  if  the  force  of  gravity  were 
as  great  here  as  it  is  in  Jupiter,  and  indicates  a  much 
greater  rate  of  increase.  Starting  from  the  upper  surface 
of  the  cloud  in  Jupiter's  atmosphere,  if  we  descend, 
not  16  miles,  but  1,600  or  16,000,  what  must  the  den- 
sity of  the  atmosphere  become  and  how  is  this  to  be 
reconciled  with  what  we  know  to  be  the  very  small 
mean  density  of  the  planet  ? 

We  are  here  in  a  dilemma  between  density  on  the 
one  hand  and  the  effects  of  gravity  on  the  other,  and 
the  only  escape  from  it  lies  in  the  assumption  that 
the  interior  of  Jupiter  is  tremendously  hot,  and  that 
this  heat  expands  the  substance  of  the  planet  in  spite 
of  the  pressure  to  which  it  is  subject,  making  a  large 
planet  with  a  low  density,  possibly  gaseous  at 
the  very  center,  but  in  its  outer  part  surrounded 
by  a  shell  of   clouds   con- 
densed from  the  gases  by 
radiating  their   heat  into 

FIG.  88-Increase  of  density  in  the  atmos-       the  Cold  of  Outer  space. 

pheres  of  Jupiter  and  the  earth.  This    is    essentially    the 

same     physical    condition 

that  we  found  for  the  sun,  and  we  may  add,  as  further 
points  of  resemblance  between  it  and  Jupiter,  that  there 
seems  to  be  a  circulation  of  matter  from  the  hot  interior  of 
the  planet  to  its  cooler  surface  that  is  more  pronounced  in 
the  southern  hemisphere  than  in  the  northern,  and  that  has 
its  periods  of  maximum  and  minimum  activity,  which,  cu- 
riously enough,  seem  to  coincide  with  periods  of  maximum 
and  minimum  sun-spot  development.  Of  this,  however,  we 
can  not  be  entirely  sure,  since  it  is  only  in  recent  years  that 
it  has  been  studied  with  sufficient  care,  and  further  obser- 
vations are  required  to  show  whether  the  agreement  is 
something  more  than  an  accidental  and  short-lived  coin- 
cidence. 

Temperature. — The   temperature    of   Jupiter  must,  of 


THE  PLANETS  223 

course,  be  much  lower  than  that  of  the  sun,  since  the  sur- 
face which  we  see  is  not  luminous  like  the  sun's  ;  but  below 
the  clouds  it  is  not  improbable  that  Jupiter  may  be  incan- 
descent, white  hot,  and  it  is  surmised  with  some  show  of 
probability  that  a  little  of  its  light  escapes  through  the 
clouds  from  time  to  time,  and  helps  to  produce  the  striking 
brilliancy  with  which  this  planet  shines. 

140.  The  satellites  of  Jupiter. — The  satellites  bear  much 
the  same  relation  to  Jupiter  that  the  moon  bears  to  the 
earth,  revolving  about  the  planet  in  accordance  with  the 
law  of  gravitation,  and  conforming  to  Kepler's  three  laws, 
as  do  the  planets  in  their  courses  about  the  sun.  Observe  in 
Fig.  86  the  position  of  satellite  No.  1  on  the  four  dates,  and 
note  how  it  oscillates  back  and  forth  from  left  to  right  of 
Jupiter,  apparently  making  a  complete  revolution  in  about 
two  days,  while  No.  4  moves  steadily  from  left  to  right  dur- 
ing the  entire  period,  and  has  evidently  made  only  a  frac- 
tion, of  a  revolution  in  the  time  covered  by  the  pictures. 
This  quicker  motion,  of  course,  means  that  No.  1  is  nearer 
to  Jupiter  than  No.  4,  and  the  numbers  given  to  the  satel- 
lites show  the  order  of  their  distances  from  the  planet. 
The  peculiar  way  in  which  the  satellites  are  grouped,  always 
standing  nearly  in  a  straight  line,  shows  that  their  orbits 
must  lie  nearly  in  the  same  plane,  and  that  this  plane,  which 
is  also  the  plane  of  the  planets'  equator,  is  turned  edgewise 
toward  the  earth. 

These  satellites  enjoy  the  distinction  of  being  the  first 
objects  ever  discovered  with  the  telescope,  having  been 
found  by  Galileo  almost  immediately  after  its  invention, 
A.  D.  1610.  It  is  quite  possible  that  before  this  time  they 
may  have  been  seen  with  the  naked  eye,  for  in  more  recent 
years  reports  are  current  that  they  have  been  seen  under 
favorable  circumstances  by  sharp-eyed  persons,  and  very 
little  telescopic  aid  is  required  to  show  them.  Look  for 
them  with  an  opera  or  field  glass.  They  bear  the  names 
lo,  Europa,  Ganymede,  Callisto,  which,  however,  are  rarely 


224 


ASTRONOMY 


used,  and,  following  the  custom  of  astronomers,  we  shall 
designate  them  by  the  Eoman  numerals  I,  II,  III,  IV. 

For  nearly  three  centuries  (1610  to  1892)  astronomers 
spoke  of  the  four  satellites  of  Jupiter ;  but  in  September, 
1892,  a  fifth  one  was  added  to  the  number  by  Professor  Bar- 
nard, who,  observing  with  the  largest  telescope  then  extant, 
found  very  close  to  Jupiter  a  tiny  object  only  ^  part  as 


/C.754  days 


FIG.  89.— Orbits  of  Jupiter's  satellites. 

bright  as  the  other  satellites,  but,  like  them,  revolving  around 
Jupiter,  a  permanent  member  of  his  system.  This  is  called 
the  fifth  satellite,  and  Fig.  89  shows  the  orbits  of  these  satel- 
lites around  Jupiter,  which  is  here  represented  on  the  same 
scale  as  the  orbits  themselves.  The  broken  line  just  inside 
the  orbit  of  I  represents  the  size  of  the  moon's  orbit.  The 
cut  shows  also  the  periodic  times  of  the  satellites  expressed 
in  days,  and  furnishes  in  this  respect  a  striking  illustra- 
tion of  the  great  mass  of  Jupiter.  Satellite  I  is  a  little 


THE   PLANETS  225 

farther  from  Jupiter  than  is  the  moon  from  the  earth,  but 
under  the  influence  of  a  greater  attraction  it  makes  the  cir- 
cuit of  its  orbit  in  1.77  days,  instead  of  taking  29.53  days, 
as  does  the  moon.  Determine  from  the  figure  by  the  method 
employed  in  §  111  how  much  more  massive  is  Jupiter  than 
the  earth. 

Small  as  these  satellites  seem  in  Fig.  86,  they  are  really 
bodies  of  considerable  size,  as  appears  from  Fig.  90,  where 
their  dimensions  are  compared  with  those  of  the  earth 
and  moon,  save  that  the  fifth  satellite  is  not  included. 
This  one  is  so  small  as  to  escape  all  attempts  at  measuring 
its  diameter,  but,  judging  from  the  amount  of  light  it  re- 
flects, the  period  printed  with  the  legend  of  the  figure 
represents  a  gross  exaggeration  of  this  satellite's  size. 


FIG.  90.— Jupiter's  satellites  compared  with  the  earth  and  moon. 


Like  the  moon,  each  of  these  satellites  may  fairly  be 
considered  a  world  in  itself,  and  as  such  a  fitting  object  of 
detailed  study,  but,  unfortunately,  their  great  distance  from 
us  makes  it  impossible,  even  with  the  most  powerful  tele- 
scope, to  see  more  upon  their  surfaces  than  occasional  vague 
markings,  which  hardly  suffice  to  show  the  rotations  of  the 
satellites  upon  their  axes. 

One  striking  feature,  however,  comes  out  from  a  study 
of  their  influence  in  disturbing  each  other's  motion  about 
Jupiter.  Their  masses  and  the  resulting  densities  of  the 
satellites  are  smaller  than  we  should  have  expected  to  find, 
the  density  being  less  than  that  of  the  moon,  and  aver- 
aging only  a  little  greater  than  the  density  of  Jupiter 


226  ASTRONOMY 

itself.  At  the  surface  of  the  third  satellite  the  force  of 
gravity  is  but  little  less  than  on  the  moon,  although  the 
moon's  density  is  nearly  twice  as  great  as  that  of  III,  and 
there  can  be  no  question  here  of  accounting  for  the  low 
density  through  expansion  by  great  heat,  as  in  the  case  of 
the  sun  and  Jupiter.  It  has  been  surmised  that  these  satel- 
lites are  not  solid  bodies,  like  the  earth  and  moon,  but  only 
shoals  of  rock  and  stone,  loosely  piled  together  and  kept 
from  packing  into  a  solid  mass  by  the  action  of  Jupiter  in 
raising  tides  within  them.  But  the  explanation  can  hardly 
be  regarded  as  an  accepted  article  of  astronomical  belief, 
although  it  is  supported  by  some  observations  which  tend 
to  show  that  the  apparent  shapes  of  the  satellites  change  un- 
der the  influence  of  the  tidal  forces  impressed  upon  them. 
141.  Eclipses  of  the  satellites, — It  may  be  seen  from  Fig. 
89  that  in  their  motion  around  the  planet  Jupiter's  satellites 
must  from  time  to  time  pass  through  his  shadow  and  be 
eclipsed,  and  that  the  shadows  of  the  satellites  will  occasion- 
ally fall  upon  the  planet,  producing  to  an  observer  upon 
Jupiter  an  eclipse  of  the  sun,  but  to  an  observer  on  the  earth 
presenting  only  the  appearance  of  a  round  black  spot  mov- 
ing slowly  across  the  face  of  the  planet.  Occasionally  also 
a  satellite  will  pass  exactly  between  the  earth  and  Jupiter, 
and  may  be  seen  projected  against  the  planet  as  a  back- 
ground. All  of  these  phenomena  are  duly  predicted  and 
observed  by  astronomers,  but  the  eclipses  are  the  only  ones 
we  need  consider  here.  The  importance  of  these  eclipses 
was  early  recognized,  and  astronomers  endeavored  to  con- 
struct a  theory  of  their  recurrence  which  would  permit 
accurate  predictions  of  them  to  be  made.  But  in  this  they 
met  with  no  great  success,  for  while  it  was  easy  enoug.h 
to  foretell  on  what  night  an  eclipse  of  a  given  satellite 
would  occur,  and  even  to  assign  the  hour  of  the  night,  it 
was  not  possible  to  make  the  predicted  minute  agree  with 
the  actual  time  of  eclipse  until  after  Roemer,  a  Danish 
astronomer  of  the  seventeenth  century,  found  where  lay  the 


THE  PLANETS  227 

trouble.  His  discovery  was,  that  whenever  the  earth  was 
on  the  side  of  its  orbit  toward  Jupiter  the  eclipses  really 
occurred  before  the  predicted  time,  and  when  the  earth 
was  on  the  far  side  of  its  orbit  they  came  a  few  minutes 
later  than  the  predicted  time.  He  correctly  inferred  thatx 
this  was  to  be  explained,  not  by  any  influence  which  the 
earth  exerted  upon  Jupiter  and  his  satellites,  but  through 
the  fact  that  the  light  by  which  we  see  the  satellite  and  its 
eclipse  requires  an  appreciable  time  to  cross  the  interven- 
ing space,  and  a  longer  time  when  the  earth  is  far  from 
Jupiter  than  when  it  is  near. 

For  half  a  century  Roemer's  views  found  little  credence, 
but  we  know  now  that  he  was  right,  and  that  on  the 
average  the  eclipses  come  8m.  18s.  early  when  the  earth  is 
nearest  to  Jupiter,  and  8m.  18s.  late  when  it  is  on  the  op- 
posite side  of  its  orbit.  This  is  equivalent  to  saying  that 
light  takes  8m.  18s.  to  cover  the  distance  from  the  sun  to 
the  earth,  so  that  at  any  moment  we  see  the  sun  not  as  it 
then  is,  but  as  it  was  8  minutes  earlier.  It  has  been  found 
possible  in  recent  years  to  measure  by  direct  experiment 
the  velocity  with  which  light  travels — 186,337  miles  per 
second — and  multiplying  this  number  by  the  498s.  (=  8m. 
18s.)  we  obtain  a  new  determination  of  the  sun's  distance 
from  the  earth.  The  product  of  the  two  numbers  is 
92,795,826,  in  very  fair  agreement  with  the  93,000,000 
miles  found  in  Chapter  X ;  but,  as  noted  there,  this  method, 
like  every  other,  has  its  weak  side,  and  the  result  may  be  a 
good  many  thousands  of  miles  in  error. 

It  is  worthy  of  note  in  this  connection  that  both  meth- 
ods of  obtaining  the  sun's  distance  which  were  given  in 
Chapter  X  involve  Kepler's  Third  Law,  while  the  result 
obtained  from  Jupiter's  satellites  is  entirely  independent 
of  this  law,  and  the  agreement  of  the  several  results  is 
therefore  good  evidence  both  for  the  truth  of  Kepler's  laws 
and  for  the  soundness  of  Eoemer's  explanation  of  the 
eclipses.  This  mode  of  proof,  by  comparing  the  numerical 


228 


ASTRONOMY 


results  furnished  by  two  or  more  different  principles,  and 
showing  that  they  agree  or  disagree,  is  of  wide  application 
and  great  importance  in  physical  science. 

SATUEI* 

142.  The  ring  of  Saturn, — In  respect  of  size  and  mass 
Saturn  stands  next  to  Jupiter,  and  although  far  inferior  to 
him  in  these  respects,  it  contains  more  material  than  all 
the  remaining  planets  combined.  But  the  unique  feature 
of  Saturn  which  distinguishes  it  from  every  other  known 

body  in  the  heavens  is 
its  ring,  which  was  long 
a  puzzle  to  the  astrono- 
mers who  first  studied 
the  planet  with  a  tele- 
scope (one  of  them  called 
Saturn  a  planet  with 
ears),  but,  was  after 
nearly  half  a  century 
correctly  understood  and 
described  by  Huyghens, 
whose  Latin  text  we 
translate  into — "  It  is 
surrounded  by  a  ring, 
thin, flat,  nowhere  touch- 
ing it,  and  making  quite 
an  angle  with  the  eclip- 
tic." 

Compare  with  this 
description  Fig.  91,  which  shows  some  of  the  appearances 
presented  by  the  ring  at  different  positions  of  Saturn  in 
its  orbit.  It  was  their  varying  aspects  that  led  Huyghens 
to  insert  the  last  words  of  his  description,  for,  if  the  plane 
of  the  ring  coincided  with  the  plane  of  the  earth's  orbit, 
then  at  all  times  the  ring  must  be  turned  edgewise  toward 
the  earth,  as  shown  in  the  middle  picture  of  the  group. 


FIG.  91. — Aspects  of  Saturn's  rings. 


THE  PLANETS 


229 


Fig.  92  shows  the  sun  and  the  orbit  of  the  earth  placed 
near  the  center  of  Saturn's  orbit,  across  whose  circumfer- 
ence are  ruled  some  oblique  lines  representing  the  plane 
of  the  ring,  the  right  end  always  tilted  up,  no  matter  where 


FIG.  92.— Aspects  of  the  ring  in  their  relation  to  Saturn's  orbital  motion. 

the  planet  is  in  its  orbit.  It  is  evident  that  an  observer 
upon  the  earth  will  see  the  N  side  of  the  ring  when  the 
planet  is  at  N  and  the  8  side  when  it  is  at  $,  as  is  shown 
in  the  first  and  third  pictures  of  Fig.  91,  while  midway  be- 
tween these  positions  the  edge  of  the  ring  will  be  presented 
to  the  earth. 

The  last  occasion  of  this  kind  was  in  October,  1891,  and 
with  the  large  telescope  of  the  Washburn  Observatory  the 


230  ASTRONOMY 

writer  at  that  time  saw  Saturn  without  a  trace  of  a  ring 
surrounding  it.  The  ring  is  so  thin  that  it  disappears 
altogether  when  turned  edgewise.  The  names  of  the  zo- 
diacal constellations  are  inserted  in  Fig.  92  in  their  proper 
direction  from  the  sun,  and  from  these  we  learn  that  the 
ring  will  disappear,  or  be  exceedingly  narrow,  whenever 
Saturn  is  in  the  constellation  Pisces  or  near  the  boundary 
line  between  Leo  and  Virgo.  It  will  be  broad  and  show  its 
northern  side  when  Saturn  is  in  Scorpius  or  Sagittarius,  and 
its  southern  face  when  the  planet  is  in  Gemini.  What  will 
be  its  appearance  in  1907  at  the  date  marked  in  the  figure? 

143.  Nature  of  the  ring. — It  is  apparent  from  Figs.  91 
and  93  that  Saturn's  ring  is  really  made  up  of  two  or  more 
rings  lying  one  inside  of  the  other  and  completely  sepa- 
rated by  a  dark  space  which,  though  narrow,  is  as  clean  and 
sharp  as  if  cut  with  a  knife.  Also,  the  inner  edge  of  the 
ring  fades  off  into  an  obscure  border  called  the  dusky  ring 
or  crape  ring.  This  requires  a  pretty  good  telescope  to 
show  it,  as  may  be  inferred  from  the  fact  that  it  escaped 
notice  for  more  than  two  centuries  during  which  the  planet 
was  assiduously  studied  with  telescopes,  and  was  discovered 
at  the  Harvard  College  Observatory  as  recently  as  1850. 

Although  the  rings  appear  oval  in  all  of  the  pictures, 
this  is  mainly  an  effect  of  perspective,  and  they  are  in  fact 
nearly  circular  with  the  planet  at  their  center.  The  ex- 
treme diameter  of  the  ring  is  172,000  miles,  and  from  this 
number,  by  methods  already  explained  (Chapter  IX),  the 
student  should  obtain  the  width  of  the  rings,  their  distance 
from  the  ball  of  the  planet,  and  the  diameter  of  the  ball. 
As  to  thickness,  it  is  evident,  from  the  disappearance  of  the 
ring  when  its  edge  is  turned  toward  the  earth,  that  it  is 
very  thin  in  comparison  with  its  diameter,  probably  not 
more  than  100  miles  thick,  although  no  exact  measurement 
of  this  can  be  made. 

From  theoretical  reasons  based  upon  the  law  of  gravita- 
tion astronomers  have  held  that  the  rings  of  Saturn  could 


FIG.  93.— Saturn. 


232  ASTRONOMY 

not  possibly  be  solid  or  liquid  bodies.  The  strains  im- 
pressed upon  them  by  the  planet's  attraction  would  tear 
into  fragments  steel  rings  made  after  their  size  and  shape. 
Quite  recently  Professor  Keeler  has  shown,  by  applying  the 
spectroscope  (Doppler's  principle)  to  determine  the  velocity 
of  the  ring's  rotation  about  Saturn,  that  the  inner  parts  of 
the  ring  move,  as  Kepler's  Third  Law  requires,  more  rapidly 
than  do  the  outer  parts,  thus  furnishing  a  direct  proof  that 
they  are  not  solid,  and  leaving  no  doubt  that  they  are  made 
up  of  separate  fragments,  each  moving  about  the  planet  in 
its  own  orbit,  like  an  independent  satellite,  but  standing  so 
close  to  its  neighbors  that  the  whole  space  reflects  the  sun- 
light as  completely  as  if  it  were  solid.  With  this  under- 
standing of  the  rings  it  is  easy  to  see  why  they  are  so  thin. 
Like  Jupiter,  Saturn  is  greatly  flattened  at  the  poles,  and 
this  flattening,  or  rather  the  protuberant  mass  about  the 
equator,  lays  hold  of  every  satellite  near  the  planet  and 
exerts  upon  it  a  direct  force  tending  to  thrust  it  down 
into  the  plane  of  the  planet's  equator  and  hold  it  there. 
The  ring  lies  in  the  plane  of  Saturn's  equator  because  each 
particle  is  constrained  to  move  there. 

The  division  of  the  ring  into  two  parts,  an  outer  and  an 
inner  ring,  is  usually  explained  as  follows :  Saturn  is  sur- 
rounded by  a  numerous  brood  of  satellites,  which  by  their 
attractions  produce  perturbations  in  the  material  compos- 
ing the  rings,  and  the  dividing  line  between  the  outer  and 
inner  rings  falls  at  the  place  where  by  the  law  of  gravita- 
tion the  perturbations  would  have  their  greatest  effect. 
The  dividing  line  between  the  rings  is  therefore  a  narrow 
lane,  2,400  miles  wide,  from  which  the  fragments  have  been 
swept  clean  away  by  the  perturbing  action  of  the  satellites. 
Less  conspicuous  divisions  are  seen  from  time  to  time  in 
other  parts  of  the  ring,  where  the  perturbations,  though 
less,  are  still  appreciable.  But  it  is  open  to  some  question 
whether  this  explanation  is  sufficient. 

The  curious  darkness  of  the  inner  or  crape  ring  is  easily 


THE  PLANETS  233 

explained.  The  particles  composing  it  are  not  packed  to- 
gether so  closely  as  in  the  outer  ring,  and  therefore  reflect 
less  sunlight.  Indeed,  so  sparsely  strewn  are  the  particles 
in  this  ring  that  it  is  in  great  measure  transparent  to  the 
sunlight,  as  is  shown  by  a  recorded  observation  of  one  of  the* 
satellites  which  was  distinctly  although  faintly  seen  while 
moving  through  the  shadow  of  the  dark  ring,  but  disap- 
peared in  total  eclipse  when  it  entered  the  shadow  cast  by 
the  bright  ring. 

144.  The  ball  of  Saturn.— The  ball  of  the  planet  is  in 
most  respects  a  smaller  copy  of  Jupiter.     With  an  equa- 
torial diameter  of  76,000  miles,  a  polar  diameter  of  69,000 
miles,  and  a  mass  95  times  that  of  the  earth,  its  density 
is  found  to  be  the  least  of  any  planet  in  the  solar  system, 
only  0.70  of  the  density  of  water,  and  about  one  half  as 
great  as  is  the  density  of  Jupiter.     The  force  of  gravity  at 
its  surface  is  only  a  little  greater  (1.18)  than  on  the  earth ; 
and  this,  in  connection  with  the  low  density,  leads,  as  in  the 
case  of  Jupiter,  to  the  conclusion  that  the  planet  must  be 
mainly  composed  of  gases  and  vapors,  very  hot  within,  but 
inclosed  by  a  shell  of  clouds  which  cuts  off  their  glow  from 
our  eyes. 

Like  Jupiter  in  another  respect,  the  planet  turns  very 
swiftly  upon  its  axis,  making  a  revolution  in  10  hours  14 
minutes,  but  up  to  the  present  it  remains  unknown  whether 
different  parts  of  the  surface  have  different  rotation  times. 

145.  The  satellites. — Saturn  is  attended  by  a  family  of 
nine  satellites,  a  larger  number  than  belongs  to  any  other 
planet,  but  with  one  exception  they  are  exceedingly  small 
and  difficult  to  observe  save  with  a  very  large  telescope. 
Indeed,  the  latest  one  to  be  discovered  was  found  in  1898  by 
means  of  the  image  which  it  impressed  upon  a  photographic 
plate,  and  it  has  never  been  seen. 

Titan,  the  largest  of  them,  is  distant  771,000  miles  from 
the  planet  and  bears  much  the  same  relation  to  Saturn  that 
Satellite  III  bears  to  Jupiter,  the  similarity  in  distance,  size, 
16 


234  ASTRONOMY 

and  mass  being  rather  striking,  although,  of  course,  the 
smaller  mass  of  Saturn  as  compared  with  Jupiter  makes  the 
periodic  time  of  Titan — 15  days  23  hours — much  greater 
than  that  of  III.  Can  you  apply  Kepler's  Third  Law  to 
the  motion  of  Titan  so  as  to  determine  from  the  data  given 
above,  the  time  required  for  a  particle  at  the  outer  or  inner 
edge  of  the  ring  to  revolve  once  around  Saturn  ? 

Japetus,  the  second  satellite  in  point  of  size,  whose  dis- 
tance from  Saturn  is  about  ten  times  as  great  as  the  moon's 
distance  from  the  earth,  presents  the  remarkable  peculiar- 
ity of  being  always  brighter  in  one  part  of  its  orbit  than 
in  another,  three  or  four  times  as  bright  when  west  of 
Saturn  as  when  east  of  it.  This  probably  indicates  that, 
like  our  own  moon,  the  satellite  turns  always  the  same  face 
toward  its  planet,  and  further,  that  one  side  of  the  satellite 
reflects  the  sunlight  much  better  than  the  other  side — i.  e., 
has  a  higher  albedo.  With  these  two  assumptions  it 
is  easily  seen  that  the  satellite  will  always  turn  toward 
the  earth  one  face  when  west,  and  the  other  face  when 
east  of  Saturn,  and  thus  give  the  observed  difference  of 
brightness. 

UKANUS  AND  NEPTUNE 

146.  Chief  characteristics.  —  The  two  remaining  large 
planets  are  interesting  chiefly  as  modern  additions  to  the 
known  members  of  the  sun's  family.  The  circumstances 
leading  to  the  discovery  of  Neptune  have  been  touched 
upon  in  Chapter  IV,  and  for  Uranus  we  need  only  note 
that  it  was  found  by  accident  in  the  year  1781  by  William 
Herschel,  who  for  some  time  after  the  discovery  considered 
it  to  be  only  a  comet.  It  was  the  first  planet  ever  discov- 
ered, all  of  its  predecessors  having  been  known  from  pre- 
historic times. 

Uranus  has  four  satellites,  all  of  them  very  faint,  which 
present  only  one  feature  of  special  importance.  Instead  of 
moving  in  orbits  which  are  approximately  parallel  to  the 


WILLIAM  HEESCHEL   (1738-1822). 


THE  PLANETS  235 

plane  of  the  ecliptic,  as  do  the  satellites  of  the  other  planets, 
their  orbit  planes  are  tipped  up  nearly  perpendicular  to  the 
planes  of  the  orbits  of  both  Uranus  and  the  earth.  The 
one  satellite  which  Neptune  possesses  has  the  same  pecul- 
iarity in  even  greater  degree,  for  its  motion  around  the 
planet  takes  place  in  the  direction  opposite  to  that  in 
which  all  the  planets  move  around  the  sun,  much  as  if  the 
orbit  of  the  satellite  had  been  tipped  over  through  an  angle 
of  150°.  Turn  a  watch  face  down  and  note  how  the  hands 
go  round  in  the  direction  opposite  to  that  in  which  they 
moved  before  the  face  was  turned  through  180°. 

Both  Uranus  and  Neptune  are  too  distant  to  allow 
much  detail  to  be  seen  upon  their  surfaces,  but  the  pres- 
ence of  broad  absorption  bands  in  their  spectra  shows  that 
they  must  possess  dense  atmospheres  quite  different  in  con- 
stitution from  the  atmosphere  of  the  earth.  In  respect  of 
density  and  the  force  of  gravity  at  their  surfaces,  they  are 
not  very  unlike  Saturn,  although  their  density  is  greater 
and  gravity  less  than  his,  leading  to  the  supposition  that 
they  are  for  the  most  part  gaseous  bodies,  but  cooler  and 
probably  more  nearly  solid  than  either  Jupiter  or  Saturn. 

Under  favorable  circumstances  Uranus  may  be  seen 
with  the  naked  eye  by  one  who  knows  just  where  to  look 
for  it.  Neptune  is  never  visible  save  in  a  telescope. 

147.  The  inner  planets. — In  sharp  contrast  with  the  giant 
planets  which  we  have  been  considering  stands  the  group 
of  four  inner  planets,  or  five  if  we  count  the  moon  as  an 
independent  body,  which  resemble  each  other  in  being  all 
small,  dense,  and  solid  bodies,  which  by  comparison  with 
the  great  distances  separating  the  outer  planets  may  fairly 
be  described  as  huddled  together  close  to  the  sun.  Their 
relative  sizes  are  shown  in  Fig.  84,  together  with  the  nu- 
merical data  concerning  size,  mass,  density,  etc.,  which  we 
have  already  found  important  for  the  understanding  of  a 
planet's  physical  condition. 


236 


ASTRONOMY 


VENUS 

148.  Appearance,— Omitting  the  earth,  Venus  is  by  far 
the  most  conspicuous  member  of  this  group,  and  when  at  its 
brightest  is,  with  exception  of  the  sun  and  moon,  the  most 
brilliant  object  in  the  sky,  and  may  be  seen  with  the  naked 
eye  in  broad  daylight  if  the  observer  knows  just  where  to 
look  for  it.  But  its  brilliancy  is  subject  to  considerable 
variations  on  account  of  its  changing  distance  from  the 


FIG.  94. — The  phases  of  Venus. — ANTONIADI. 

earth,  and  the  apparent  size  of  its  disk  varies  for  the  same 
reason,  as  may  be  seen  from  Fig.  94.  These  drawings  bring 
out  well  the  phases  of  the  planet,  and  the  student  should 
determine  from  Fig.  17  what  are  the  relative  positions  in 
their  orbits  of  the  earth  and  Venus  at  which  the  planet 
would  present  each  of  these  phases.  As  a  guide  to  this, 
observe  that  the  dark  part  of  Venus's  earthward  side  is 
always  proportional  in  area  to  the  angle  at  Venus  between 
the  earth  and  sun.  In  the  first  picture  of  Fig.  94  about 


THE   PLANETS  237 

two  thirds  of  the  surface  corresponding  to  the  full  hemi- 
sphere of  the  planet  is  dark,  and  the  angle  at  Venus 
between  earth  and  sun  is  therefore  two  thirds  of  180° — i.  e., 
120°.  In  Fig.  17  find  a  place  on  the  orbit  of  Venus  from 
which  if  lines  be  drawn  to  the  sun  and  earth,  as  there 
shown,  the  angle  between  them  will  be  120°.  Make  a  simi- 
lar construction  for  the  fourth  picture  in  Fig.  94.  Which 
of  these  two  positions  is  farther  from  the  earth  ?  How  do 
the  distances  compare  with  the  apparent  size  of  Venus  in 
the  two  pictures  ?  What  is  the  phase  of  Venus  to-day  ? 

The  irregularities  in  the  shading  of  the  illuminated 
parts  of  the  disk  are  too  conspicuous  in  Fig.  94,  on  account 
of  difficulties  of  reproduction;  these  shadings  are  at  the 
best  hard  to  see  in  the  telescope,  and  distinct  permanent 
markings  upon  the  planet  are  wholly  lacking.  This  absence 
of  markings  makes  almost  impossible  a  determination  of 
the  planet's  time  of  rotation  about  its  axis,  and -astrono- 
mers are  divided  in  this  respect  into  two  parties,  one  of 
which  maintains  that  Venus,  like  the  earth,  turns  upon  its 
axis  in  some  period  not  very  different  from  24  hours,  while 
the  other  contends  that,  like  the  moon,  it  turns  always  the 
same  face  toward  the  center  of  its  orbit,  making  a  rotation 
upon  its  axis  in  the  same  period  in  which  it  makes  a  revo- 
lution about  the  sun.  The  reason  why  no  permanent  mark- 
ings are  to  be  seen  on  this  planet  is  easily  found.  Like 
Jupiter  and  Saturn,  its  atmosphere  is  at  all  times  heavily 
cloud-laden,  so  that  we  seldom,  if  ever,  see  down  to  the 
level  of  its  solid  parts.  There  is,  however,  no  reason  here 
to  suppose  the  interior  parts  hot  and  gaseous.  It  is  much 
more  probable  that  Venus,  like  the  earth,  possesses  a  solid 
crust  whose  temperature  we  should  expect  to  be  consider- 
ably higher  than  that  of  the  earth,  because  Venus  is  nearer 
the  sun.  But  the  cloud  layer  in  its  atmosphere  must  modify 
the  temperature  in  some  degree,  and  we  have  practically 
no  knowledge  of  the  real  temperature  conditions  at  the 
surface  of  the  planet. 


238  ASTRONOMY 

It  is  the  clouds  of  Venus  which  in  great  measure  are 
responsible  for  its  marked  brilliancy,  since  they  are  an  ex- 
cellent medium  for  reflecting  the  sunlight,  and  give  to  its 
surface  an  albedo  greater  than  that  of  any  other  planet, 
although  Saturn  is  nearly  equal  to  it. 

Of  course,  the  presence  of  such  cloud  formations  indi- 
cates that  Venus  is  surrounded  by  a  dense  atmosphere,  and 
we  have  independent  evidence  of  this  in  the  shape  of  its 
disk  when  the  planet  is  very  nearly  between  the  earth  and 
sun.  The  illuminated  part,  from  tip  to  tip  of  the  horns? 
then  stretches  more  than  halfway  around  the  planet's  cir- 
cumference, and  shows  that  a  certain  amount  of  light  must 
have  been  refracted  through  its  atmosphere,  thus  making 
the  horns  of  the  crescent  appear  unduly  prolonged.  This 
atmosphere  is  shown  by  the  spectroscope  to  be  not  unlike 
that  of  the  earth,  although  probably  more  dense. 

MERCURY 

149.  Chief  characteristics. — Mercury,  on  account  of  its 
nearness  to  the  sun,  is  at  all  times  a  difficult  object  to  ob- 
serve, and  Copernicus,  who  spent  most  of  his  life  in  Poland, 
is  said,  despite  all  his  efforts,  to  have  gone  to  his  grave  with- 
out ever  seeing  it.  In  our  more  southern  latitude  it  can 
usually  be  seen  for  about  a  fortnight  at  the  time  of  each 
elongation — i.  e.,  when  at  its  greatest  angular  distance  from 
the  sun — and  the  student  should  find  from  Fig.  16  the  time 
at  which  the  next  elongation  occurs  and  look  for  the  planet, 
shining  like  a  star  of  the  first  magnitude,  low  down  in  the 
sky  just  after  sunset  or  before  sunrise,  according  as  the 
elongation  is  to  the  east  or  west  of  the  sun.  When  seen  in 
the  morning  sky  the  planet  grows  brighter  day  after  day 
until  it  disappears  in  the  sun's  rays,  while  in  the  evening 
sky  its  brilliancy  as  steadily  diminishes  until  the  planet  is 
lost.  It  should  therefore  be  looked  for  in  the  evening  as 
soon  as  possible  after  it  emerges  from  the  sun's  rays. 

Mercury,  as  the  smallest  of  the  planets,  is  best  compared 


THE  PLANETS  239 

with  the  moon,  which  it  does  not  greatly  surpass  in  size 
and  which  it  strongly  resembles  in  other  respects.  Careful 
comparisons  of  the  amount  of  light  reflected  by  the  planet 
in  different  parts  of  its  orbit  show  not  only  that  its  albedo 
agrees  very  closely  with  that  of  the  moon,  but  also  that  its 
light  changes  with  the  varying  phase  of  the  planet  in  al- 
most exactly  the  same  way  as  the  amount  of  moonlight 
changes.  We  may  therefore  infer  that  its  surface  is  like 
that  of  the  moon,  a  rough  and  solid  one,  with  few  or  no 
clouds  hanging  over  it,  and  most  probably  covered  with 
very  little  or  no  atmosphere.  Like  Venus,  its  rotation  pe- 
riod is  uncertain,  with  the  balance  of  probability  favoring 
the  view  that  it  rotates  upon  its  axis  once  in  88  days,  and 
therefore  always  turns  the  same  face  toward  the  sun. 

If  such  is  the  case,  its  climate  must  be  very  peculiar : 
one  side  roasted  in  a  perpetual  day,  where  the  direct  heat- 
ing power  of  the  sun's  rays,  when  the  planet  is  at  perihelion, 
is  ten  times  as  great  as  on  the  moon,  and  which  six  weeks 
later,  when  the  planet  is  at  its  farthest  from  the  sun,  has 
fallen  off  to  less  than  half  of  this.  On  the  opposite  side  of 
the  planet  there  must  reign  perpetual  night  and  perpetual 
cold,  mitigated  by  some  slight  access  of  warmth  from  the 
day  side,  and  perhaps  feebly  imitating  the  rapid  change  of 
season  which  takes  place  on  the  day  side  of  the  planet. 
This  view,  however,  takes  no  account  of  a  possible  devia- 
tion of  the  planet's  axis  from  being  perpendicular  to  the 
plane  of  its  orbit,  or  of  the  librations  which  must  be  pro- 
duced by  the  great  eccentricity  of  the  orbit,  either  of  which 
would  complicate  without  entirely  destroying  the  ideal 
conditions  outlined  above. 

MAKS 

150.  Appearance. — The  one  remaining  member  of  the 
inner  group,  Mars,  has  in  recent  years  received  more  atten- 
tion than  any  other  planet,  and  the  newspapers  and  maga- 
zines have  announced  marvelous  things  concerning  it :  that 


240 


ASTRONOMY 


it  is  inhabited  by  a  race  of  beings  superior  in  intelligence 
to  men  ;  that  the  work  of  their  hands  may  be  seen  upon 
the  face  of  the  planet ;  that  we  should  endeavor  to  com- 
municate with  them,  if  indeed  they  are  not  already  sending 
messages  to  us,  etc. — all  of  which  is  certainly  important, 
if  true,  but  it  rests  upon  a  very  slender  foundation  of  evi- 
dence, a  part  of  which  we  shall  have  to  consider. 

Beginning  with  facts  of  which  there  is  no  doubt,  this 
ruddy-colored  planet,  which  usually  shines  about  as  brightly 

as  a  star  of  the  first  mag- 
nitude, sometimes  dis- 
plays more  than  tenfold 
this  brilliancy,  surpass- 
ing every  other  planet 
save  Venus  and  present- 
ing at  these  times  espe- 
cially favorable  opportu- 
nities for  the  study  of 
its  surface.  The  expla- 
nation of  this  increase 
of  brilliancy  is,  of  course, 
that  the  planet  approach- 
es unusually  near  to  the 
earth,  and  we  have  al- 
ready seen  from  a  con- 
sideration of  Fig.  17 
that  this  can  only  hap- 
pen in  the  months  of  August  and  September.  The  last 
favorable  epoch  of  this  kind  was  in  1894.  From  Fig.  17 
the  student  should  determine  when  the  next  one  will 
come. 

Fig.  95  presents  nine  drawings  of  the  planet  made  at 
one  of  the  epochs  of  close  approach  to  the  earth,  and  shows 
that  its  face  bears  certain  faint  markings  which,  though 
inconspicuous,  are  fixed  and  permanent  features  of  the 
planet.  The  dark  triangular  projection  in  the  lower  half 


FIG.  95.— Mars.— SCHAEBERLE. 


THE   PLANETS 


241 


of  the  second  drawing  was  seen  and  sketched  by  Huyghens. 
1659  A.  D.  In  Fig.  96  some  of  these  markings  are  shown 
much  more  plainly,  but  Fig.  95  gives  a  better  idea  of  their 
usual  appearance  in  the  telescope. 

151.  Rotation. — It  may  be  seen  readily  enough,  from  a 
comparison  of  the  first  two  sketches  of  Fig.  95,  that  the 
planet  rotates  about  an 
axis,  and  from  a  more 
extensive  study  it  is 
found  to  be  very  like 
the  earth  in  this  re- 
spect, turning  once  in 
24h.  37m.  around  an 
axis  tipped  from  being 
perpendicular  to  the 
plane  of  its  orbit  about 
a  degree  and  a  half 
more  than  is  the  earth's 
axis.  Since  it  is  this 
inclination  of  the  axis 
which  is  the  cause  of 
changing  seasons  upon 
the  earth,  there  must 
be  similar  changes, 

winter  and  summer,  as  well  as  day  and  night,  upon  Mars, 
only  each  season  is  longer  there  than  here  in  the  same  pro- 
portion that  its  year  is  longer  than  ours — i.  e.,  nearly  two 
to  one.  It  is  summer  in  the  northern  hemisphere  of  Mars 
whenever  the  sun,  as  seen  from  Mars,  stands  in  that  con- 
stellation which  is  nearest  the  point  of  the  sky  toward 
which  the  planet's  axis  points.  But  this  axis  points  toward 
the  constellation  Cygnus,  and  Alpha  Cygni  is  the  bright 
star  nearest  the  north  pole  of  Mars.  As  Pisces  is  the 
zodiacal  constellation  nearest  to  Cygnus,  it  must  be  sum- 
mer in  the  northern  hemisphere  of  Mars  when  the  sun  is  in 
Pisces,  or,  turning  the  proposition  about,  it  must  be  summer 


FIG.  96.— Four  views  of  Mars  differing  90°  in 
longitude. — BARNARD. 


242 


ASTRONOMY 


in  the  southern  hemisphere  of  Mars  when  the  planet,  as 
seen  from  the  sun,  lies  in  the  direction  of  Pisces. 

152.  The  polar  caps. — One  effect  of  the  changing  seasons 
upon  Mars  is  shown  in  Fig.  97,  where  we  have  a  series  of 
drawings  of  the  region  about  its  south  pole  made  in  1894, 
on  dates  between  May  21st  and  December  10th.  Show 
from  Fig.  16  that  during  this  time  it  was  summer  in  the 
region  here  shown.  Mars  crossed  the  prime  radius  in  1894 
on  September  5th.  The  striking  thing  in  these  pictures  is 
the  white  spot  surrounding  the  pole,  which  shrinks  in  size 

from  the  beginning  to 
near  the  end  of  the  se- 
ries, and  then  disappears 
altogether.  The  spot 
came  back  again  a  year 
later,  and  like  a  similar 
spot  at  the  north  pole  of 
the  planet  it  waxes  in  the 
winter  and  wanes  during 
the  summer  of  Mars  in 
endless  succession. 

Sir  W.  Herschel,  who 
studied  these  appear- 
ances a  century  ago,  com- 
pared them  with  the  snow 
fields  which  every  winter 

FIG.  97.— The  south  polar  cap  of  Mars  in  ..  .  , 

1894.-BABNARD.  spread  out  from  the  re- 

gion around  the  terres- 
trial pole,  and  in  the  summer  melt  and  shrink,  although 
with  us  they  do  not  entirely  disappear.  This  explanation  of 
the  polar  caps  of  Mars  has  been  generally  accepted  among 
astronomers,  and  from  it  we  may  draw  one  interesting  con- 
clusion :  the  temperature  upon  Mars  between  summer  and 
winter  oscillates  above  and  below  the  freezing  point  of 
water,  as  it  does  in  the  temperate  zones  of  the  earth.  But 
this  conclusion  plunges  us  into  a  serious  difficulty.  The 


THE  PLANETS  243 

temperature  of  the  earth  is  made  by  the  sun,  and  at  the 
distance  of  Mars  from  the  sun  the  heating  effect  of  the 
latter  is  reduced  to  less  than  half  what  it  is  at  the  earth, 
so  that,  if  Mars  is  to  be  kept  at  the  same  temperature  as 
the  earth,  there  must  be  some  peculiar  means  for  storing 
the  solar  heat  and  using  it  more  economically  than  is  done 
here.  Possibly  there  is  some  such  mechanism,  although 
no  one  has  yet  found  it,  and  some  astronomers  are  very 
confident  that  it  does  not  exist,  and  assert  that  the  com- 
parison of  the  polar  caps  with  snow  fields  is  misleading, 
and  that  the  temperature  upon  Mars  must  be  at  least  100°, 
and  perhaps  200°  or  more,  below  zero. 

153.  Atmosphere  and  climate. — In  this  connection  one 
feature  of  Mars  is  of  importance.  The  markings  upon  its 
surface  are  always  visible  when  turned  toward  the  earth, 
thus  showing  that  the  atmosphere  contains  no  such  amount 
of  cloud  as  does  our  own,  but  on  the  whole  is  decidedly 
clear  and  sunny,  and  presumably  much  less  dense  than 
ours.  AVe  have  seen  in  comparing  the  earth  and  the  moon 
how  important  is  the  service  which  the  earth's  atmosphere 
renders  in  storing  the  sun's  heat  and  checking  those  great 
vicissitudes  of  temperature  to  which  the  moon  is  subject ; 
and  with  this  in  mind  we  must  regard  the  smaller  density 
and  cloudless  character  of  the  atmosphere  of  Mars  as  un- 
favorable to  the  maintenance  there  of  a  temperature  like 
that  of  the  earth.  Indeed,  this  cloudlessness  must  mean 
one  of  two  things :  either  the  temperature  is  so  low  that 
vapors  can  not  exist  in  any  considerable  quantity,  or  the 
surface  of  Mars  is  so  dry  that  there  is  little  water  or  other 
liquid  to  be  evaporated.  The  latter  alternative  is  adopted 
by  those  astronomers  who  look  upon  the  polar  caps  as  true 
snow  fields,  which  serve  as  the  chief  reservoir  of  the  planet's 
water  supply,  and  who  find  in  Fig.  98  evidence  that  as  the 
snow  melts  and  the  water  flows  away  over  the  flat,  dry  sur- 
face of  the  planet,  vegetation  springs  up,  as  shown  by  the 
dark  markings  on  the  disk,  and  gradually  dies  out  with 


244 


ASTRONOMY 


the  advancing  season.  Note  that  in  the  first  of  these  pic- 
tures the  season  upon  Mars  corresponds  to  the  end  of  May 
with  us,  and  in  the  last  picture  to  the  beginning  of  August, 
a  period  during  which  in  much  of  our  western  country  the 
luxuriant  vegetation  of  spring  is  burned  out  by  the  scorch- 
ing sun.  From  this  point  of  view  the  permanent  dark 
spots  are  the  low-lying  parts  of  the  planet's  surface,  in 
which  at  all  times  there  is  a  sufficient  accumulation  of 
water  to  support  vegetable  life. 

154.  The  canals.— In  Fig.  98  the  lower  part  of  the  disk 
of  Mars  shows  certain  faint  dark  lines  which  are  generally 
called  canals,  and  in  Plate  III  there  is  given  a  map  of  Mars 


FIG.  98.— The  same  face  of  Mars  at  three  different  seasons.— LOWELL. 

showing  many  of  these  canals  running  in  narrow,  dusky 
streaks  across  the  face  of  the  planet  according  to  a  pattern 
almost  as  geometrical  as  that  of  a  spider's  web.  This  must 
not  be  taken  for  a  picture  of  the  planet's  appearance  in  a 
telescope.  No  man  ever  saw  Mars  look  like  this,  but  the 
map  is  useful  as  a  plain  representation  of  things  dimly 
seen.  Some  of  the  regions  of  this  map  are  marked  Mare 
(sea),  in  accordance  with  the  older  view  which  regarded 
the  darker  parts  of  the  planet — and  of  themotm— as  bodies 
of  water,  but  this  is  now  known  to  be  an  error  in  both 
cases.  The  curved  surface  of  a  planet  can  not  be  accurately 
reproduced  upon  the  flat  surface  of  paper,  but  ifi  always 
more  or  less  distorted  by  the  various  methods  of/"  project- 
ing "  it  which  are  in  use.  Compare  the  map/of  Mars  in 


THE  PLANETS  245 

Plate  III  with  Fig.  99,  in  which  the  projection  represents 
very  well  the  equatorial  parts  of  the  planet,  but  enormously 
exaggerates  the  region  arou  nd  the  poles. 

It  is  a  remarkable  feature  of  the  canals  that  they  all 
begin  and  end  in  one  of  these  dark  parts  of  the  planetV 
surface ;  they  show  no  loose  ends  lying  on  the  bright  parts 
of  the  planet.  Another  even  more  remarkable  feature  is 
that  while  the  larger  canals  are  permanent  features  of  the 
planet's  surface,  they  at  times  appear  "  doubled  " — i.  e.,  in 
place  of  one  canal  two  parallel  ones  side  by  side,  lasting 
for  a  time  and  then  giving  place  again  to  a  single  canal. 

It  is  exceedingly  difficult  to  frame  any  reasonable  ex- 
planation of  these  canals  and  the  varied  appearances  which 
they  present.  The  source  of  the  wild  speculations  about 
Mars,  to  which  reference  is  made  above,  is  to  be  found  in 
the  suggestion  frequently  made,  half  in  jest  and  half  in 
earnest,  that  the  canals  are  artificial  water  courses  con- 
structed upon  a  scale  vastly  exceeding  any  public  works 
upon  the  earth,  and  testifying  to  the  presence  in  Mars  of 
an  advanced  civilization.  The  distinguished  Italian  as- 
tronomer, Schiaparelli,  who  has  studied  these  formations 
longer  than  any  one  else,  seems  inclined  to  regard  them  as 
water  courses  lined  on  either  side  by  vegetation,  which 
flourishes  as  far  back  from  the  central  channel  as  water 
can  be  supplied  from  it — a  plausible  enough  explanation  if 
the  fundamental  difficulty  about  temperature  can  be  over- 
come. 

155.  Satellites. — In  1877,  one  of  the  times  of  near  ap- 
proach, Professor  Hall,  of  Washington,  discovered  two  tiny 
satellites  revolving  about  Mars  in  orbits  so  small  that  the 
nearer  one,  Phobos,  presents  the  remarkable  anomaly  of 
completing  the  circuit  of  its  orbit  in  less  time  than  the 
planet  takes  for  a  rotation  about  its  axis.  This  satellite,  in 
fact,  makes  three  revolutions  in  its  orbit  while  the  planet 
turns  once  upon  its  axis,  and  it  therefore  rises  in  the  west 
and  sets  in  the  east,  as  seen  from  Mars,  going  from  one 


3 S       SS?g2o2SS?3S? 


THE  PLANETS  247 

horizon  to  the  other  in  a  little  less  than  6  hours.  The 
other  satellite,  Deimos,  takes  a  few  hours  more  than  a  day 
to  make  the  circuit  of  its  orhit,  but  the  difference  is  so 
small  that  it  remains  continuously  above  the  horizon  of 
any  given  place  upon  Mars  for  more  than  60  hours  at  a 
time,  and  during  this  period  runs  twice  through  its  com- 
plete set  of  phases — new,  first  quarter,  full,  etc.  In  ordi- 
nary telescopes  these  satellites  can  be  seen  only  under  espe- 
cially favorable  circumstances,  and  are  far  too  small  to 
permit  of  any  direct  measurement  of  their  size.  The 
amount  of  light  which  they  reflect  has  been  compared 
with  that  of  Mars  and  found  to  be  as  much  inferior  to  it 
as  is  Polaris  to  two  full  moons,  and,  judging  from  this  com- 
parison, their  diameters  can  not  much  exceed  a  half  dozen 
miles,  unless  their  albedo  is  far  less  than  that  of  Mars, 
which  does  not  seem  probable. 

THE  ASTEKOIDS 

156.  Minor  planets. — These  may  be  dismissed  with  few 
words.  There  are  about  500  of  them  known,  all  discovered 
since  the  beginning  of  the  nineteenth  century,  and  new 
ones  are  still  found  every  year.  No  one  pretends  to 
remember  the  names  which  have  been  assigned  them,  and 
they  are  commonly  represented  by  a  number  inclosed  in  a 
circle,  showing  the  order  in  which  they  were  discovered — 
e.  g.,  Q  =  Ceres,  @  —  Eros,  etc.  For  the  most  part  they 
are  little  more  than  chips,  world  fragments,  adrift  in  space, 
and  naturally  it  was  the  larger  and  brighter  of  them  that 
were  first  discovered.  The  size  of  the  first  four  of  them — 
Ceres,  Pallas,  Juno,  and  Vesta — compared  with  the  size  of 
the  moon,  according  to  Professor  Barnard,  is  shown  in  Fig. 
100.  The  great  majority  of  them  must  be  much  smaller 
than  the  smallest  of  these,  perhaps  not  more  than  a  score 
of  miles  in  diameter. 

A  few  of  the  asteroids  present  problems  of  special  in- 
terest, such  as  Eros,  on  account  of  its  close  approach  to  the 


248 


ASTRONOMY 


earth ;  Polyhymnia,  whose  very  eccentric  orbit  makes  it  a 
valuable  means  for  determining  the  mass  of  Jupiter,  etc.; 
but  these  are  special  cases  and  the  average  asteroid  now 
receives  scant  attention,  although  half  a  century  ago,  when 
only  a  few  of  them  were  known,  they  were  regarded  with 
much  interest,  and  the  discovery  of  a  new  one  was  an  event 
of  some  consequence. 

It  was  then  a  favorite  speculation  that  they  were  in  fact 
fragments  of  an  ill-fated  planet  which  once  filled  the  gap 

between  the  orbits  of  Mars 
and  Jupiter,  but  which,  by 
some  mischance,  had  been 
blown  into  pieces.  This  is 
now  known  to  be  well-nigh 
impossible,  for  every  frag- 
ment which  after  the  explo- 
sion moved  in  an  elliptical 
orbit,  as  all  the  asteroids  do 
move,  would  be  brought 
back  once  in  every  revolu- 
tion to  the  place  of  the  ex- 
plosion, and  all  the  asteroid 
orbits  must  therefore  inter- 
sect at  this  place.  But  there  is  no  such  common  point  of 
intersection. 

157.  Life  on  the  planets. — There  is  a  belief  firmly 
grounded  in  the  popular  mind,  and  not  without  its  ad- 
vocates among  professional  astronomers,  that  the  planets 
are  inhabited  by  living  and  intelligent  beings,  and  it  seems 
proper  at  the  close  of  this  chapter  to  inquire  briefly  how 
far  the  facts  and  principles  here  developed  are  consistent 
with  this  belief,  and  what  support,  if  any,  they  lend  to  it. 

At  the  outset  we  must  observe  that  the  word  life  is  an 
elastic  term,  hard  to  define  in  any  satisfactory  way,  and  yet 
standing  for  something  which  we  know  here  upon  the 
earth.  It  is  this  idea,  our  familiar  though  crude  knowl- 


FIG.  100.— The  size  of  the  first  four 
asteroids. — BARNARD. 


THE  PLANETS  249 

edge  of  life,  which  lies  at  the  root  of  the  matter.  Life,  if 
it  exists  in  another  planet,  must  be  in  its  essential  char- 
acter like  life  upon  the  earth,  and  must  at  least  possess 
those  features  which  are  common  to  all  forms  of  terrestrial 
life.  It  is  an  abuse  of  language  to  say  that  life  in  Mars- 
may  be  utterly  unlike  life  in  the  earth ;  if  it  is  absolutely 
unlike,  it  is  not  life,  whatever  else  it  may  be.  Now,  every 
form  of  life  found  upon  the  earth  has  for  its  physical  basis 
a  certain  chemical  compound,  called  protoplasm,  which 
can  exist  and  perpetuate  itself  only  within  a  narrow  range 
of  temperature,  roughly  speaking,  between  0°  and  100° 
centigrade,  although  these  limits  can  be  considerably  over- 
stepped for  short  periods  of  time.  Moreover,  this  proto- 
plasm can  be  active  only  in  the  presence  of  water,  or  water 
vapor,  and  we  may  therefore  establish  as  the  necessary  con- 
ditions for  the  continued  existence  and  reproduction  of 
life  in  any  place  that  its  temperature  must  not  be  perma- 
nently above  100°  or  below  0°,  C.,  and  water  must  be  pres- 
ent in  that  place  in  some  form. 

With  these  conditions  before  us  it  is  plain  that  life  can 
not  exist  in  the  sun  on  account  of  its  high  temperature. 
It  is  conceivable  that  active  and  intelligent  beings,  salaman- 
ders, might  exist  there,  but  they  could  not  properly  be  said 
to  live.  In  Jupiter  and  Saturn  the  same  condition  of  high 
temperature  prevails,  and  probably  also  in  Uranus  and 
Xeptune,  so  that  it  seems  highly  improbable  that  any  of 
these  planets  should  be  the  home  of  life. 

Of  the  inner  planets,  Mercury  and  the  moon  seem  desti- 
tute of  any  considerable  atmospheres,  and  are  therefore 
lacking  in  the  supply  of  water  necessary  for  life,  and  the 
same  is  almost  certainly  true  of  all  the  asteroids.  There 
remain  Venus,  Mars,  and  the  satellites  of  the  outer  planets, 
which  latter,  however,  we  must  drop  from  consideration  as 
being  too  little  known.  On  Venus  there  is  an  atmosphere 
probably  containing  vapor  of  water,  and  it  is  well  within 
the  range  of  possibility  that  liquid  water  should  exist  upon 
17 


250  ASTRONOMY 

the  surface  of  this  planet  and  that  its  temperature  should 
fall  within  the  prescribed  limits.  It  would,  however,  be 
straining  our  actual  knowledge  to  affirm  that  such  is  the 
case,  or  to  insist  that  if  such  were  the  case,  life  would  ne- 
cessarily exist  upon  the  planet. 

On  Mars  we  encounter  the  fundamental  difficulty  of 
temperature  already  noted  in  §  152.  If  in  some  unknown 
way  the  temperature  is  maintained  sufficiently  high  for  the 
polar  caps  to  be  real  snow,  thawing  and  forming  again  with 
the  progress  of  the  seasons,  the  necessary  conditions  of  life 
would  seem  to  be  fulfilled  here  and  life  if  once  introduced 
upon  the  planet  might  abide  and  flourish.  But  of  positive 
proof  that  such  is  the  case  we  have  none. 

On  the  whole,  our  survey  lends  little  encouragement  to 
the  belief  in  planetary  life,  for  aside  from  the  earth,  of  all 
the  hundreds  of  bodies  in  the  solar  system,  not  one  is  found 
in  which  the  necessary  conditions  of  life  are  certainly  ful- 
filled, and  only  two  exist  in  which  there  is  a  reasonable 
probability  that  these  conditions  may  be  satisfied. 


CHAPTEE  XII 

COMETS    AND    METEORS 

158.  Visitors  in  the  solar  system.— All  of  the  objects — 
sun,  moon,  planets,  stars — which  we  have  thus  far  had  to 
consider,  are  permanent  citizens  of  the  sky,  and  we  have  no 
reason  to  suppose  that  their  present  appearance  differs  ap- 
preciably from  what  it  was  1,000  years  or  10,000  years  ago. 
But  there  is  another  class  of  objects — comets,  meteors — 
which  appear  unexpectedly,  are  visible  for  a  time,  and  then 
vanish  and  are  seen  no  more.  On  account  of  this  temporary 
character  the  astronomers  of  ancient  and  mediaeval  times 
for  the  most  part  refused  to  regard  them  as  celestial  bodies 
but  classed  them  along  with  clouds,  fogs,  Jack-o'-lanterns, 
and  fireflies,  as  exhalations  from  the  swamps  or  the  vol- 
cano ;  admitting  them  to  be  indeed  important  as  harbingers 
of  evil  to  mankind,  but  having  no  especial  significance  for 
the  astronomer. 

The  comet  of  1018  A.  D.  inspired  the  lines — 

"  Eight  things  there  be  a  Comet  brings, 
When  it  on  high  doth  horrid  range  : 
Wind,  Famine,  Plague,  and  Death  to  Kings, 

War,  Earthquakes,  Floods,  and  Direful  Change," 

which,  according  to  White  (History  of  the  Doctrine  of 
Comets),  were  to  be  taught  in  all  seriousness  to  peasants 
and  school  children. 

It  was  by  slow  degrees,  and  only  after  direct  measure- 
ments of  parallax  had  shown  some  of  them  to  be  more  dis- 
tant than  the  moon,  that  the  tide  of  old  opinion  was  turned 
and  comets  were  transferred  from  the  sublunary  to  the 

251 


252 


ASTRONOMY 


celestial  sphere,  and  in  more  recent  times  meteors  also 
have  been  recognized  as  coming  to  us  from  outside  the 
earth.  A  meteor,  or  shooting  star  as  it  is  often  called,  is 
one  of  the  commonest  of  phenomena,  and  one  can  hardly 
watch  the  sky  for  an  hour  on  any  clear  and  moonless  night 
without  seeing  several  of  those  quick  flashes  of  light  which 
look  as  if  some  star  had  suddenly  left  its  place,  dashed 
swiftly  across  a  portion  of  the  sky  and  then  vanished.  It 
is  this  misleading  appearance  that  prohably  is  responsible 
for  the  name  shooting  star. 

159.  Comets, — Comets  are  less  common  and  much  longer- 
lived  than  meteors,  lasting  usually  for  several  weeks,  and 
may  be  visible  night  after  night  for  many  months,  but 
never  for  many  years,  at  a  time.  During  the  last  decade 


FIG.  101.— Douati's  comet.— BOND. 


there  is  no  year  in  which  less  than  three  comets  have 
appeared,  and  1898  is  distinguished  by  the  discovery  of 
ten  of  these  bodies,  the  largest  number  ever  found  in 
one  year.  On  the  average,  we  may  expect  a  new  comet  to 


COMETS  AND  METEORS 


253 


be  found  about  once  in  every  ten  weeks,  but  for  the  most 
part  they  are  small  affairs,  visible  only  in  the  telescope,  and 
a  fine  large  one,  like  Donati's  comet  of  1858  (Fig.  101),  or 
the  Great  Comet  of  Septem- 
ber, 1882,  which  was  visible  in 
broad  daylight  close  beside  the 
sun,  is  a  rare  spectacle,  and  as 
striking  and  impressive  as  it 
is  rare. 

Note  in  Fig.  102  the  great 
variety  of  aspect  presented 
by  some  of  the  more  famous 
comets,  which  are  here  repre- 
sented upon  a  very  small  scale. 

Fig.  103  is  from  a  photo- 
graph of  one  of  the  faint 
comets  of  the  year  1893,  which 
appears  here  as  a  rather  feeble 
streak  of  light  amid  the  stars 
which  are  scattered  over  the 
background  of  the  picture. 

An  apparently  detached  portion  of  this  comet  is  shown  at 
the  extreme  left  of  the  picture,  looking  almost  like  another 
independent  comet.  The  clean,  straight  line  running  diag- 
onally across  the  picture  is  the  flash  of  a  bright  meteor 
that  chanced  to  pass  within  the  range  of  the  camera  while 
the  comet  was  being  photographed. 

A  more  striking  representation  of  a  moderately  bright 
telescopic  comet  is  contained  in  Figs.  104  and  105,  which 
present  two  different  views  of  the  same  comet,  showing  a 
considerable  change  in  its  appearance.  A  striking  feature 
of  Fig.  105  is  the  star  images,  which  are  here  drawn  out  into 
short  lines  all  parallel  with  each  other.  During  the  expos- 
ure of  2h.  20m.  required  to  imprint  this  picture  upon  the 
photographic  plate,  the  comet  was  continually  changing  its 
position  among  the  stars  on  account  of  its  orbital  motion, 


FIG.  102. — Some  famous  comets. 


254 


ASTRONOMY 


and  the  plate  was  therefore  moved  from  time  to  time,  so  as 
to  follow  the  comet  and  make  its  image  always  fall  at  the 
same  place.  Hence  the  plate  was  continually  shifted  rela- 
tive to  the  stars  whose  images,  drawn  out  into  lines,  show 
the  direction  in  which  the  plate  was  moved — i.  e.,  the  direc- 
tion in  which  the  comet  was  moving  across  the  sky.  The 
same  effect  is  shown  in  the  other  photographs,  but  less 
conspicuously  than  here  on  account  of  their  shorter  expos- 
ure times. 

These  pictures  all  show  that  one  end  of  the  comet  is 
brighter  and  apparently  more  dense  than  the  other,  and  it 

is  customary  to  call 
this  bright  part  the 
head  of  the  comet, 
while  the  brushlike 
appendage  that 
streams  away  from 
it  is  called  the 
comet's  tail. 

160.  The  parts 
of  a  comet. — It  is 
not  every  comet 
that  has  a  tail, 
though  all  the 
large  ones  do,  and 
in  Fig.  103  the  de- 
tached piece  of 
cometary  matter  at 
the  left  of  the 
picture  represents 

very  well  the  appearance  of  a  tailless  comet,  a  rather  large 
but  not  very  bright  star  of  a  fuzzy  or  hairy  appearance. 
The  word  comet  means  long-haired  or  hairy  star.  Some- 
thing of  this  vagueness  of  outline  is  found  in  all  comets, 
whose  exact  boundaries  are  hard  to  define,  instead  of  being 
sharp  and  clean-cut  like  those  of  a  planet  or  satellite. 


FIG.  103.— Brooke's  comet,  November  13,  1893. 
BARNARD. 


COMETS  AND  METEORS  255 

Often,  however,  there  is  found  in  the  head  of  a  comet  a 
much  more  solid  appearing  part,  like  the  round  white  ball 
at  the  center  of  Fig.  106,  which  is  called  the  nucleus  of 


FIG.  104.— Swift's  comet,  April  17,  1892.— BAKNARD. 

the  comet,  and  appears  to  be  in  some  sort  the  center  from 
which  its  activities  radiate.  As  shown  in  Figs.  106  and 
107,  the  nucleus  is  sometimes  surrounded  by  what  are 
called  envelopes,  which  have  the  appearance  of  successive 
wrappings  or  halos  placed  about  it,  and  odd,  spurlike  pro- 
jections, called  jets,  are  sometimes  found  in  connection 
with  the  envelopes  or  in  place  of  them.  These  figures  also 
show  what  is  quite  a  common  characteristic  of  large 
comets,  a  dark  streak  running  down  the  axis  of  the  tail, 
showing  that  the  tail  is  hollow,  a  mere  shell  surrounding 
empty  space. 

The  amount  of  detail  shown  in  Figs.  106  and  107  is, 
however,  quite  exceptional,  and  the  ordinary  comet  is  much 
more  like  Fig.  103  or  104.  Even  a  great  comet  when  it 


256  ASTRONOMY 

first  appears  is  not  unlike  the  detached  fragment  in  Fig. 
103,  a  faint  and  roundish  patch  of  foggy  light  which  grows 
through  successive  stages  to  its  maximum  estate,  develop- 
ing a  tail,  nucleus,  envelopes,  etc.,  only  to  lose  them  again 
as  it  shrinks  and  finally  disappears. 

161.  The  orbits  of  comets,— It  will  be  remembered  that 
Newton  found,  as  a  theoretical  consequence  of  the  law  of 
gravitation,  that  a  body  moving  under  the  influence  of  the 
sun's  attraction  might  have  as  its  orbit  any  one  of  the 
conic  sections,  ellipse,  parabola,  or  hyperbola,  and  among 
the  400  and  more  comet  orbits  which  have  been  deter- 
mined every  one  of  these  orbit  forms  appear,  but  curiously 
enough  there  is  not  a  hyperbola  among  them  which,  if 
drawn  upon  paper,  could  be  distinguished  by  the  unaided 


FIG.  105.— Swift's  comet,  April  24,  1892.— BARNARD. 

eye  from  a  parabola,  and  the  ellipses  are  all  so  long  and 
narrow,  not  one  of  them  being  so  nearly  round  as  is  the 
most  eccentric  planet  orbit,  that  astronomers  are  accus- 
tomed to  look  upon  the  parabola  as  being  the  normal  type 


COMETS  AND  METEORS 


257 


of  comet  orbit,  and  to  regard  a  comet  whose  motion  differs 
much  from  a  parabola  as  being  abnormal  and  calling  for 
some  special  explanation. 

The  fact  that  comet  orbits  are  parabolas,  or  differ  but 
little  from  them,  explains  at  once  the  temporary  character 
and  speedy  disappearance 
of  these  bodies.  They 
are  visitors  to  the  solar 
system  and  visible  for 
only  a  short  time,  because 
the  parabola  in  which 
they  travel  is  not  a  closed 
curve,  and  the  comet,  hav- 
ing passed  once  along 
that  portion  of  it  near  the 
earth  and  the  sun,  moves 
off  along  a  path  which 
ever  thereafter  takes  it 
farther  and  farther  away, 
beyond  the  limit  of  visi- 
bility. The  development 
of  the  comet  during  the 
time  it  is  visible,  the 
growth  and  disappearance 

of  tail,  nucleus,  etc.,  depend  upon  its  changing  distance 
from  the  sun,  the  highest  development  and  most  complex 
structure  being  presented  when  it  is  nearest  to  the  sun. 

Fig.  108  shows  the  path  of  the  Great  Comet  of  1882 
during  the  period  in  which  it  was  seen,  from  September  3, 
1882,  to  May  26, 1883.  These  dates— IX,  3,  and  V,  26— are 
marked  in  the  figure  opposite  the  parts  of  the  orbit  in 
which  the  comet  stood  at  those  times.  Similarly,  the  posi- 
tions of  the  earth  in  its  orbit  at  the  beginning  of  Septem- 
ber, October,  Xovember,  etc.,  are  marked  by  the  Roman 
numerals  IX,  X,  XI,  etc.  The  line  S  V  shows  the  direction 
from  the  sun  to  the  vernal  equinox,  and  S&  is  the  line 


FIG.  106.— Head  of  Coggia's  comet, 
July  13,  1874.— BOND. 


258 


ASTRONOMY 


along  which  the  plane  of  the  comet's  orbit  intersects  the 
plane  of  the  earth's  orbit — i.  e.,  it  is  the  line  of  nodes  of  the 
comet  orbit.  Since  the  comet  approached  the  sun  from 
the  south  side  of  the  ecliptic,  all  of  its  orbit,  save  the  little 
segment  which  falls  to  the  left  of  $Q,  lies  below  (south)  of 
the  plane  of  the  earth's  orbit,  and  the  part  which  would 
be  hidden  if  this  plane  were  opaque  is  represented  by  a 
broken  line. 

162.  Elements  of  a  comet's  orbit,— There  is  a  theorem  of 
geometry  to  the  effect  that  through  any  three  points  not 
in  the  same  straight  line  one  circle,  and  only  one,  can  be 
drawn.  Corresponding  to  this  there  is  a  theorem  of  celes- 
tial mechanics,  that  through  any  three  positions  of  a  comet 

one  conic  section,  and 
only  one,  can  be  passed 
along  which  the  comet 
can  move  in  accordance 
with  the  law  of  gravita- 
tion. This  conic  section 
is,  of  course,  its  orbit,  and 
at  the  discovery  of  a  com- 
et astronomers  always 
hasten  to  observe  its  po- 
sition in  the  sky  on  dif- 
ferent nights  in  order  to 
obtain  the  three  positions 
(right  ascensions  and  de- 
clinations) necessary  for 
determining  the  particu- 
lar orbit  in  which  it 
moves.  The  circle,  to 
which  reference  was  made 
above,  is  completely  as- 
certained and  defined  when  we  know  its  radius  and  the 
position  of  its  center.  A  parabola  is  not  so  simply  defined, 
and  five  numbers,  called  the  elements  of  its  orbit,  are 


FIG.  107.— Head  of  Donati's  comet,  Septem- 
ber 30,  October  2,  1858.— BOND. 


COMETS  AND  METEORS 


259 


required  to  fix  accurately  a  comet's  path  around  the  sun. 
Two  of  these  relate  to  the  position  of  the  line  of  nodes  and 
the  angle  which  the  orbit  plane  makes  with  the  plane  of  the 
ecliptic  ;  a  third  fixes  the  direction  of  the  axis  of  the  orbit 


FIG.  108.— Orbits  of  the  earth  and  the 
Great  Comet  of  1882. 


in  its  plane,  and  the  remaining  two,  which  are  of  more 
interest  to  us,  are  the  date  at  which  the  comet  makes  its 
nearest  approach  to  the  sun  (perihelion  passage)  and  its 
distance  from  the  sun  at  that  date  (perihelion  distance). 
The  date,  September  17th,  placed  near  the  center  of  Fig. 
108,  is  the  former  of  these  elements,  while  the  latter,  which 
is  too  small  to  be  accurately  measured  here,  may  be  found 
from  Fig.  109  to  be  0.82  of  the  sun's  diameter,  or,  in  terms 
of  the  earth's  distance  from  the  sun,  C.008. 

Fig.  109  shows  on  a  large  scale  the  shape  of  that  part  of 
the  orbit  near  the  sun  and  gives  the  successive  positions  of 
the  comet,  at  intervals  of  T2¥  of  a  day,  on  September  16th 
and  17th,  showing  that  in  less  than  10  hours — 17.0  to  17.4 
— the  comet  swung  around  the  sun  through  an  angle  of 


260 


ASTRONOMY 


more  than  240°.  When  at  its  perihelion  it  was  moving 
with  a  velocity  of  300  miles  per  second  !  This  very  unusual 
velocity  was  due  to  the  comet's  extraordinarily  close  ap- 
proach to  the  sun.  The  earth's  velocity  in  its  orbit  is  only 
19  miles  per  second,  and  the  velocity  of  any  comet  at  any 
distance  from  the  sun,  provided  its  orbit  is  a  parabola,  may 
be  found  by  dividing  this  number  by  the  square  root  of 
half  the  comet's  distance — e.  g.,  300  miles  per  second  equals 
19-^0.004. 

Most  of  the  visible  comets  have  their  perihelion  dis- 
tances included  between  ^  and  f  of  the  earth's  distance 
from  the  sun,  but  occasionally  one  is  found,  like  the 
second  comet  of  1885,  whose  nearest  approach  to  the  sun 


FIG.  109.— Motion  of  the  Great  Comet  of  1882  in  passing  around  the  sun. 

lies  far  outside  the  earth's  orbit,  in  this  case  half-way 
out  to  the  orbit  of  Jupiter;  but  such  a  comet  must  be  a 
very  large  one  in  order  to  be  seen  at  all  from  the  earth. 


COMETS  AND  METEORS 


261 


FIG.  110.— The  Great  Comet  of  1843. 

There  is,  however,  some  reason  for  believing  that  the  num- 
ber of  comets  which  move  around  the  sun  without  ever 
coming  inside  the  orbit  of  Jupiter,  or  even  that  of  Saturn, 
is  much  larger  than  the  number  of  those  which  come  close 
enough  to  be  discovered  from  the  earth.  In  any  case  we 
are  reminded  of  Kepler's  saying,  that  comets  in  the  sky  are 
as  plentiful  as  fishes  in  the  sea,  which  seems  to  be  very  little 
exaggerated  when  we  consider  that,  according  to  Kleiber, 
out  of  all  the  comets  which  enter  the  solar  system  probably 
not  more  than  2  or  3  per  cent  are  ever  discovered. 

163.  Dimensions  of  comets, — The  comet  whose  orbit  is 
shown  in  Figs.  108  and  109  is  the  finest  and  largest  that 
has  appeared  in  recent  years.  Its  tail,  which  at  its  maxi- 
mum extent  would  have  more  than  bridged  the  space  be- 
tween sun  and  earth  (100,000,000  miles),  is  made  very  much 
too  short  in  Fig.  109,  but  when  at  its  best  was  probably  not 
inferior  to  that  of  the  Great  Comet  in  1843,  shown  in  Fig. 


262  ASTRONOMY 

110.  As  we  shall  see  later,  there  is  a  peculiar  and  special 
relationship  between  these  two  comets. 

The  head  of  the  comet  of  1882  was  not  especially  large 
— about  twice  the  diameter  of  the  ball  of  Saturn — but  its 
nucleus,  according  to  an  estimate  made  by  Dr.  Elkin  when 
it  was  very  near  perihelion,  was  as  large  as  the  moon.  The 
head  of  the  comet  shown  in  Fig.  107  was  too  large  to  be 
put  in  the  space  between  the  earth  and  the  moon,  and  the 
Great  Comet  of  1811  had  a  head  considerably  larger  than 
the  sun  itself.  From  these  colossal  sizes  down  to  the 
smallest  shred  just  visible  in  the  telescope,  comets  of  all 
dimensions  may  be  found,  but  the  smaller  the  comet  the 
less  the  chance  of  its  being  discovered,  and  a  comet  as  small 
as  the  earth  would  probably  go  unobserved  unless  it  ap- 
proached very  close  to  us. 

164.  The  mass  of  a  comet, — There  is  no  known  case  in 
which  the  mass  of  a  comet  has  ever  been  measured,  yet 
nothing  about  them  is  more  sure  than  that  they  are  bodies 
with  mass  which  is  attracted  by  the  sun  and  the  planets, 
and  which  in  its  turn  attracts  both  sun  and  planets  and 
produces  perturbations  in  their  motion.  These  perturba- 
tions are,  however,  too  small  to  be  measured,  although  the 
corresponding  perturbations  in  the  comet's  motion  are 
sometimes  enormous,  and  since  these  mutual  perturbations 
are  proportional  to  the  masses  of  comet  and  planet,  we  are 
forced  to  say  that,  by  comparison  with  even  such  small 
bodies  as  the  moon  or  Mercury,  the  mass  of  a  comet  is 
utterly  insignificant,  certainly  not  as  great  as  a  ten-thou- 
'"salrdth  part  of  the  mass  of  the  earth.  In  the  case  of  the 
Great  Comet  of  1882,  if  we  leave  its  hundred  million  miles 
of  tail  out^pf  account  and  suppose  the  entire  mass  condensed 
into  its  head,  we  find  by  a  little  computation  that  the  aver- 
age density  of^  the  head  under  these  circumstances  must 
have  been  less\  than  T^Vo-  Part  of  tne  density  of  air.  In 
ordinary  laboratory  practice  this  would  be  called  a  pretty 
good  vacuum. 


COMETS  AND  METEORS  263 

A  striking  observation  made  on  September  17,  1882, 
goes  to  confirm  the  very  small  density  of  this  comet.  It 
is  shown  in  Fig.  109  that  early  on  that  day  the  comet 
crossed  the  line  joining  earth  and  sun,  and  therefore  passed 
in  transit  over  the  sun's  disk.  Two  observers  at  the  Cape 
of  Good  Hope  saw  the  comet  approach  the  sun,  and  fol- 
lowed it  with  their  telescopes  until  the  nucleus  actually 
reached  the  edge  of  the  sun  and  disappeared,  behind  it  as 
they  supposed,  for  no  trace  of  the  comet,  not  even  its 
nucleus,  could  be  seen  against  the  sun,  although  it  was  care- 
fully looked  for.  Now,  the  figure  shows  that  the  comet 
passed  between  the  earth  and  sun,  and  its  densest  parts 
were  therefore  too  attenuated  to  cut  off  any  perceptible 
fraction  of  the  sun's  rays.  In  other  cases  stars  have  been 
seen  through  the  head  of  a  comet,  shining  apparently  with 
undimmed  luster,  although  in  some  cases  they  seem  to 
have  been  slightly  refracted  out  of  their  true  positions. 

165.  Meteors. — Before  proceeding  further  with  the  study 
of  comets  it  is  well  to  turn  aside  and  consider  their  hum- 
bler relatives,  the  shooting  stars.  On  some  clear  evening, 
when  the  moon  is  absent  from  the  sky,  watch  the  heavens 
for  an  hour  and  count  the  meteors  visible  during  that  time. 
Note  their  paths,  the  part  of  the  sky  where  they  appear 
and  where  they  disappear,  their  brightness,  and  whether 
they  all  move  with  equal  swiftness.  Out  of  such  simple 
observations  with  the  unaided  eye  there  has  grown  a  large 
and  important  branch  of  astronomical  science,  some  parts 
of  which  we  shall  briefly  summarize  here. 

A  particular  meteor  is  a  local  phenomenon  seen  over 
only  a  small  part  of  the  earth's  surface,  although  occasion- 
ally a  very  big  and  bright  one  may  travel  and  be  visible 
over  a  considerable  territory.  Such  a  one  in  December, 
1876,  swept  over  the  United  States  from  Kansas  to  Penn- 
sylvania, and  was  seen  from  eleven  different  States.  But  the 
ordinary  shooting  star  is  much  less  conspicuous,  and,  as  we 
know  from  simultaneous  observations  made  at  neighboring 


264:  ASTRONOMY 

places,  it  makes  its  appearance  at  a  height  of  some  75  miles 
above  the  earth's  surface,  occupies  something  like  a  second 
in  moving  over  its  path,  and  then  disappears  at  a  height 
of  ahout  50  miles  or  more,  although  occasionally  a  big  one 
comes  down  to  the  very  surface  of  the  earth  with  force 
sufficient  to  bury  itself  in  the  ground,  from  which  it  may 
be  dug  up,  handled,  weighed,  and  turned  over  to  the  chem- 
ist to  be  analyzed.  The  pieces  thus  found  show  that  the 
big  meteors,  at  least,  are  masses  of  stone  or  mineral ;  iron 
is  quite  commonly  found  in  them,  as  are  a  considerable 
number  of  other  terrestrial  substances  combined  in  rather 
peculiar  ways.  But  no  chemical  element  not  found  on  the 
earth  has  ever  been  discovered  in  a  meteor. 

166.  Nature  of  meteors. — The  swiftness  with  which  the 
meteors  sweep  down  shows  that  they  must  come  from  out- 
side the  earth,  for  even  half  their  velocity,  if  given  to  them 
by  some  terrestrial  volcano  or  other  explosive  agent,  would 
send  them  completely  away  from  the  earth  never  to  return. 
We  must  therefore  look  upon  them  as  so  many  projectiles, 
bullets,  fired  against  the  earth  from  some  outside  source 
and  arrested  in  their  motion  by  the  earth's  atmosphere, 
which  serves  as  a  cushion  to  protect  the  ground  from  the 
bombardment  which  would  otherwise  prove  in  the  highest 
degree  dangerous  to  both  property  and  life.  The  speed  of 
the  meteor  is  checked  by  the  resistance  which  the  atmos- 
phere offers  to  its  motion,  and  the  energy  represented  by 
that  speed  is  transformed  into  heat,  which  in  less  than  a 
second  raises  the  meteor  and  the  surrounding  air  to  incan- 
descence, melts  the  meteor  either  wholly  or  in  part,  and 
usually  destroys  its  identity,  leaving  only  an  impalpable 
dust,  which  cools  off  as  it  settles  slowly  through  the  lower 
atmosphere  to  the  ground.  The  heating  effect  of  the  air's 
resistance  is  proportional  to  the  square  of  the  meteor's 
velocity,  and  even  at  such  a  moderate  speed  as  1  mile  per 
second  the  effect  upon  the  meteor  is  the  same  as  if  it  stood 
still  in  a  bath  of  red-hot  air.  Now,  the  actual  velocity  of 


COMETS  AND  METEORS  265 

meteors  through  the  air  is  often  30  or  40  times  as  great  as 
this,  and  the  corresponding  effect  of  the  air  in  raising  its 
temperature  is  more  than  1,000  times  that  of  red  heat. 
Small  wonder  that  the  meteor  is  brought  to  lively  incan- 
descence and  consumed  even  in  a  fraction  of  a  second. 

167.  The  number  of  meteors. — A  single  observer  may 
expect  to  see  in  the  evening  hours  about  one  meteor  every 
10  minutes  on  the  average,  although,  of  course,  in  this 
respect  much  irregularity  may  occur.  Later  in  the  night 
they  become  more  frequent,  and  after  2  A.  M.  there  are 
about  three  times  as  many  to  be  seen  as  in  the  evening 
hours.  But  no  one  person  can  keep  a  watch  upon  the 
whole  sky,  high  and  low,  in  front  and  behind,  and  experi- 
ence shows  that  by  increasing  the  number  of  observers  and 
assigning  to  each  a  particular  part  of  the  sky,  the  total 
number  of  meteors  counted  may  be  increased  about  five- 
fold. So,  too,  the  observers  at  any  one  place  can  keep  an 
effective  watch  upon  only  those  meteors  which  come  into  the 
earth's  atmosphere  within  some  moderate  distance  of  their 
station,  say  50  or  100  miles,  and  to  watch  every  part  of  that 
atmosphere  would  require  a  large  number  of  stations,  esti- 
mated at  something  more  than  10,000,  scattered  systemat- 
ically over  the  whole  face  of  the  earth.  If  we  piece  to- 
gether the  several  numbers  above  considered,  taking  14  as 
a  fair  average  of  the  hourly  number  of  meteors  to  be  seen 
by  a  single  observer  at  all  hours  of  the  night,  we  shall  find 
for  the  total  number  of  meteors  encountered  by  the  earth 
in  24  hours,  14  X  5  X  10,000  x  24  =  16,800,000.  Without 
laying  too  much  stress  upon  this  particular  number,  we 
may  fairly  say  that  the  meteors  picked  up  by  the  earth 
every  day  are  to  be  reckoned  by  millions,  and  since  they 
come  at  all  seasons  of  the  year,  we  shall  have  to  admit  that 
the  region  through  which  the  earth  moves,  instead  of  being 
empty  space,  is  really  a  dust  cloud,  each  individual  particle 
of  dust  being  a  prospective  meteor. 

On  the  average  these  individual  particles  are  very  small 
18 


266  ASTRONOMY 

and  very  far  apart ;  a  cloud  of  silver  dimes  each  about  250 
miles  from  its  nearest  neighbor  is  perhaps  a  fair  representa- 
tion of  their  average  mass  and  distance  from  each  other, 
but,  of  course,  great  variations  are  to  be  expected  both  in  the 
size  and  in  the  frequency  of  the  particles.  There  must  be 
great  numbers  of  them  that  are  too  small  to  make  shooting 
stars  visible  to  the  naked  eye,  and  such  are  occasionally 
seen  darting  by  chance  across  the  field  of  view  of  a  tele- 
scope. 

168.  The  zodiacal  light  is  an  effect  probably  due  to  the 
reflection  of  sunlight  from  the  myriads  of  these  tiny  meteors 
which  occupy  the  space  inside  the  earth's  orbit.     It  is  a 
faint  and  diffuse  stream  of  light,  something  like  the  Milky 
Way,  which  may  be  seen  in  the  early  evening  or  morning 
stretching  up  from  the  sunrise   or   sunset   point   of  the 
horizon  along  the  ecliptic  and   following   its   course   for 
many  degrees,  possibly  around  the  entire  circumference  of 
the  sky.     It  may  be  seen  at  any  season  of  the  year,  although 
it  shows  to  the  best  advantage  in  spring   evenings   and 
autumn  mornings.     Look  for  it. 

169.  Great  meteors. — But  there  are  other  meteors,  veri- 
table fireballs  in  appearance,  far  more  conspicuous  and  im- 
posing than  the  ordinary  shooting  star.     Such  a  one  ex- 
ploded over  the  city  of  Madrid,  Spain,  on  the  morning  of 
February  10,  1896,  giving  in  broad  sunlight  "  a  brilliant 
flash  which  was  followed  ninety  seconds  later  by  a  succes- 
sion of  terrific  noises  like  the  discharge  of  a  battery  of 
artillery."    Fig.  110  shows  a  large  meteor  which  was  seen 
in  California  in  the  early  evening  of  July  27,  1894,  and 
which  left  behind  it  a  luminous  trail  or  cloud  visible  for 
more  than  half  an  hour. 

Not  infrequently  large  meteors  are  found  traveling 
together,  two  or  three  or  more  in  company,  making  their 
appearance  simultaneously  as  did  the  California  meteor  of 
October  22,  1896,  which  is  described  as  triple,  the  trio  fol- 
lowing one  another  like  a  train  of  cars,  and  Arago  cites  an 


COMETS  AND  METEORS 


26T 


instance,  from  the  year  1830,  where  within  a  short  space  of 
time  some  forty  brilliant  meteors  crossed  the  sky,  all  mov- 
ing in  the  same  direction  with  a  whistling  noise  and  dis- 
playing in  their  flight  all  the  colors  of  the  rainbow. 

The  mass  of  great  meteors  such  as  these  must  be  meas- 
ured in  hundreds  if  not  thousands  of  pounds,  and  stories 
are  current,  although  not 
very  well  authenticated,  of 
even  larger  ones,  many  tons 
in  weight,  having  been  found 
partially  buried  in  the  ground. 
Of  meteors  which  have  been 
actually  seen  to  fall  from  the 
sky,  the  largest  single  frag- 
ment recovered  weighs  about 
500  pounds,  but  it  is  only  a 
fragment  of  the  original  me- 
teor, which  must  have  been 
much  more  massive  before  it 
was  broken  up  by  collision 
with  the  atmosphere. 

170.  The  velocity  of  me- 
teors.— Every  meteor,  big  or 
little,  is  subject  to  the  law  of 
gravitation,  and  before  it  en- 
counters the  earth  must  be 
moving  in  some  kind  of  orbit 
having  the  sun  at  its  focus, 
the  particular  species  of  orbit — ellipse,  parabola,  hyperbola 
— depending  upon  the  velocity  and  direction  of  its  motion. 
Xow,  the  direction  in  which  a  meteor  is  moving  can  be 
determined  without  serious  difficulty  from  observations  of 
its  apparent  path  across  the  sky  made  by  two  or  more  ob- 
servers, but  the  velocity  can  not  be  so  readily  found,  since 
the  meteors  go  too  fast  for  any  ordinary  process  of  timing. 
But  by  photographing  one  of  them  two  or  three  times  on 


FIG.  111.— The  California  meteor  of 
July  27, 1894. 


268  ASTRONOMY 

the  same  plate,  with  an  interval  of  only  a  tenth  of  a  second 
between  exposures,  Dr.  Elkin  has  succeeded  in  showing,  in 
a  few  cases,  that  their  velocities  varied  from  20  to  25  miles 
per  second,  and  must  have  been  considerably  greater  than 
this  before  the  meteors  encountered  the  earth's  atmosphere. 
This  is  a  greater  velocity  than  that  of  the  earth  in  its  orbit, 
19  miles  per  second,  as  might  have  been  anticipated,  since 
the  mere  fact  that  meteors  can  be  seen  at  all  in  the  evening 
hours  shows  that  some  of  them  at  least  must  travel  consid- 
erably faster  than  the  earth,  for,  counting  in  the  direction 
of  the  earth's  motion,  the  region  of  sunset  and  evening  is 
always  on  the  rear  side  of  the  earth,  and  meteors  in  order 
to  strike  this  region  must  overtake  it  by  their  swifter 
motion.  We  have  here,  in  fact,  the  reason  why  meteors 
are  especially  abundant  in  the  morning  hours ;  at  this  time 
the  observer  is  on  the  front  side  of  the  earth  which  catches 
swift  and  slow  meteors  alike,  while  the  rear  is  pelted  only 
by  the  swifter  ones  which  follow  it. 

A  comparison  of  the  relative  number  of  morning  and 
evening  meteors  makes  it  probable  that  the  average  meteor 
moves,  relative  to  the  sun,  with  a  velocity  of  about  26  miles 
per  second,  which  is  very  approximately  the  average  velocity 
of  comets  when  they  are  at  the  earth's  distance  from  the 
sun.  Astronomers,  therefore,  consider  meteors  as  well  as 
comets  to  have  the  parabola  and  the  elongated  ellipse  as 
their  characteristic  orbits. 

171.  Meteor  showers— The  radiant. — There  is  evident 
among  meteors  a  distinct  tendency  for  individuals,  to  the 
number  of  hundreds  or  even  hundreds  of  millions,  to 
travel  together  in  flocks  or  swarms,  all  going  the  same  way 
in  orbits  almost  exactly  alike.  This  gregarious  tendency  is 
made  manifest  not  only  by  the  fact  that  from  time  to  time 
there  are  unusually  abundant  meteoric  displays,  but  also 
by  a  striking  peculiarity  of  their  behavior  at  such  times. 
The  meteors  all  seem  to  come  from  a  particular  part  of  the 
heavens,  as  if  here  were  a  hole  in  the  sky  through  which 


COMETS  AND  METEORS  269 

they  were  introduced,  and  from  which  they  flow  away  in 
every  direction,  even  those  which  do  not  visibly  start  from 
this  place  having  paths  among  the  stars  which,  if  prolong- 
ing backward,  would  pass  through  it.  The  cause  of  this 
appearance  may  be  understood  from  Fig.  112,  which  repre-^ 


FIG.  112. — Explanation  of  the  radiant  of  a  meteoric  shower. — DENNING. 

sents  a  group  of  meteors  moving  together  along  parallel 
paths  toward  an  observer  at  D.  Traveling  unseen  above 
the  earth  until  they  encounter  the  upper  strata  of  its  at- 
mosphere, they  here  become  incandescent  and  speed  on  in 
parallel  paths,  -?,  #,  3,  ^,  5,  0,  which,  as  seen  by  the  observer, 
are  projected  back  against  the  sky  into  luminous  streaks 
that,  as  is  shown  by  the  arrowheads,  #,  c,  d,  all  seem  to 
radiate  from  the  point  a — i.  e.,  from  the  point  in  the  sky 
whose  direction  from  the  observer  is  parallel  to  the  paths 
of  the  meteors. 

Such  a  display  is  called  a  meteor  shower,  and  the  point 
a  is  called  its  radiant.  Note  how  those  meteors  which 
appear  near  the  radiant  all  have  short  paths,  while  those 
remote  from  it  in  the  sky  have  longer  ones.  Query  :  As 
the  night  wears  on  and  the  stars  shift  toward  the  west,  will 


270 


ASTKONOMY 


the  radiant  share  in  their  motion  or  will  it  be  left  behind  ? 
Would  the  luminous  part  of  the  path  of  any  of  these  me- 
teors pass  across  the  radiant  from  one  side  to  the  other  ? 
Is  such  a  crossing  of  the  radiant  possible  under  any  circum- 
stances ?  Fig.  113  shows  how  the  meteor  paths  are  grouped 
around  the  radiant  of  a  strongly  marked  shower.  Select 
from  it  the  meteors  which  do  not  belong  to  this  shower. 


FIG.  113. — The  radiant  of  a  meteoric  shower,  showing  also  the  paths  of  three  meteors 
which  do  not  belong  to  this  shower.— DENNING. 

Many  hundreds  of  these  radiants  have  been  observed  in 
the  sky,  each  of  which  represents  an  orbit  along  which  a 
group  of  meteors  moves,  and  the  relation  of  one  of  these 


COMETS  AND  METEOBS  271 

orbits  to  that  of  the  earth  is  shown  in  Fig.  114.  The  orbit 
of  the  meteors  is  an  ellipse  extending  out  beyond  the  orbit 
of  Uranus,  but  so  eccentric  that  a  part  of  it  comes  inside 
the  orbit  of  the  earth,  and  the  figure  shows  only  that  part 
of  it  which  lies  nearest  the  sun.  The  Eoman  numerals 


Fia.  114.— The  orbits  of  the  earth  and  the  November  meteors. 

which  are  placed  along  the  earth's  orbit  show  the  position 
of  the  earth  at  the  beginning  of  the  tenth  month,  eleventh 
month,  etc.  The  meteors  flow  along  their  orbit  in  a  long 
procession,  whose  direction  of  motion  is  indicated  by  the 
arrow  heads,  and  the  earth,  coming  in  the  opposite  direc- 
tion, plunges  into  this  stream  and  receives  the  meteor 
shower  when  it  reaches  the  intersection  of  the  two  orbits. 
The  long  arrow  at  the  left  of  the  figure  represents  the 
direction  of  motion  of  another  meteor  shower  which 
encounters  the  earth  at  this  point. 

Can  you  determine  from  the  figure  answers  to  the  fol- 
lowing questions  ?  On  what  day  of  the  year  will  the  earth 
meet  each  of  these  showers?  Will  the  radiant  points  of 
the  showers  lie  above  or  below  the  plane  of  the  earth's 


272  ASTRONOMY 

orbit  ?  Will  these  meteors  strike  the  front  or  the  rear  of 
the  earth  ?  Can  they  be  seen  in  the  evening  hours  ? 

From  many  of  the  radiants  year  after  year,  upon  the 
same  day  or  week  in  each  year,  there  comes  a  swarm  of 
shooting  stars,  showing  that  there  must  be  a  continuous 
procession  of  meteors  moving  along  this  orbit,  so  that  some 
are  always  ready  to  strike  the  earth  whenever  it  reaches 
the  intersection  of  its  orbit  with  theirs.  Such  is  the  expla- 
nation of  the  shower  which  appears  each  year  in  the  first 
half  of  August,  and  whose  meteors  are  sometimes  called 
Perseids,  because  their  radiant  lies  in  the  constellation 
Perseus,  and  a  similar  explanation  holds  for  all  the  star 
showers  which  are  repeated  year  after  year. 

172.  The  Leonids. — There  is,  however,  a  kind  of  star 
shower,  of  which  the  Leonids  (radiant  in  Leo)  is  the  most 
conspicuous  type,  in  which  the  shower,  although  repeated 
from  year  to  year,  is  much  more  striking  in  some  years 
than  in  others.  Thus,  to  quote  from  the  historian  :  "  In 
1833  the  shower  was  well  observed  along  the  whole  eastern 
coast  of  North  America  from  the  Gulf  of  Mexico  to  Hali- 
fax. The  meteors  were  most  numerous  at  about  5  A.  M.  on 
November  13th,  and  the  rising  sun  could  not  blot  out  all 
traces  of  the  phenomena,  for  large  meteors  were  seen  now  and 
then  in  full  daylight.  Within  the  scope  that  the  eye  could 
contain,  more  than  twenty  could  be  seen  at  a  time  shooting 
in  every  direction.  Not  a  cloud  obscured  the  broad  expanse, 
and  millions  of  meteors  sped  their  way  across  in  every 
point  of  the  compass.  Their  coruscations  were  bright, 
gleaming,  and  incessant,  and  they  fell  thick  as  the  flakes  in 
the  early  snows  of  December."  But,  so  far  as  is  known,  none 
of  them  reached  the  ground.  An  illiterate  man  on  the  fol- 
lowing day  remarked  :  "  The  stars  continued  to  fall  until 
none  were  left.  I  am  anxious  to  see  how  the  heavens  will 
appear  this  evening,  for  I  believe  we  shall  see  no  more  stars." 

An  eyewitness  in  the  Southern  States  thus  describes 
the  effect  of  this  shower  upon  the  plantation  negroes  : 


COMETS  AND  METEORS  2Y3 

"  Upward  of  a  hundred  lay  prostrate  upon  the  ground, 
some  speechless  and  some  with  the  bitterest  cries,  but  with 
their  hands  upraised,  imploring  God  to  save  the  world  and 
them.  The  scene  was  truly  awful,  for  never  did  rain  fall 
much  thicker  than  the  meteors  fell  toward  the  earth — east, 
west,  north,  and  south  it  was  the  same."  In  the  preceding 
year  a  similar  but  feebler  shower  from  the  same  radiant 
created  much  alarm  in  France,  and  through  the  old  historic 
records  its  repetitions  may  be  traced  back  at  intervals  of  33 
or  34  years,  although  with  many  interruptions,  to  October 
12,  902,  0.  S.,  when  "  an  immense  number  of  falling  stars 
were  seen  to  spread  themselves  over  the  face  of  the  sky 
like  rain." 

Such  a  star  shower  differs  from  the  one  repeated  every 
year  chiefly  in  the  fact  that  its  meteors,  instead  of  being 
drawn  out  into  a  long  procession,  are  mainly  clustered  in  a 
single  flock  which  may  be  long  enough  to  require  two  or 
three  or  four  years  to  pass  a  given  point  of  its  orbit,  but 
which  is  far  from  extending  entirely  around  it,  so  that  me- 
teors from  this  source  are  abundant  only  in  those  years  in 
which  the  flock  is  at  or  near  the  intersection  of  its  orbit 
with  that  of  the  earth.  The  fact  that  the  Leonid  shower  is 
repeated  at  intervals  of  33  or  34  years  (it  appeared  in  1799, 
1832-'33,  1866-'67)  shows  that  this  is  the  "  periodic  time  " 
in  its  orbit,  which  latter  must  of  course  be  an  ellipse,  and 
presumably  a  long  and  narrow  one.  It  is  this  orbit  which 
is  shown  in  Fig.  114,  and  the  student  should  note  in  this 
figure  that  if  the  meteor  stream  at  the  point  where  it  cuts 
through  the  plane  of  the  earth's  orbit  were  either  nearer  to 
or  farther  from  the  sun  than  is  the  earth  there  could  be  no 
shower ;  the  earth  and  the  meteors  would  pass  by  without  a 
collision.  Now,  the  meteors  in  their  motion  are  subject  to 
perturbations,  particularly  by  the  large  planets  Jupiter, 
Saturn,  and  Uranus,  which  slightly  change  the  meteor  orbit, 
and  it  seems  certain  that  the  changes  thus  produced  will 
sometimes  thrust  the  swarm  inside  or  outside  the  orbit  of 


274  ASTRONOMY 

the  earth,  and  thus  cause  a  failure  of  the  shower  at  times 
when  it  is  expected.  The  meteors  were  due  at  the  crossing 
of  the  orbits  in  November,  1899  and  1900,  and,  although  a 
few  were  then  seen,  the  shower  was  far  from  being  a  bril- 
liant one,  and  its  failure  was  doubtless  caused  by  the  outer 
planets,  which  switched  the  meteors  aside  from  the  path  in 
which  they  had  been  moving  for  a  century.  Whether  they 
will  be  again  switched  back  so  as  to  produce  future  showers 
is  at  the  present  time  uncertain. 

173.  Capture  of  the  Leonids.— But  a  far  more  striking 
effect  of  perturbations  is  to  be  found  in  Fig.  115,  which 
shows  the  relation  of  the  Leonid  orbit  to  those  of  the  prin- 
cipal planets,  and  illustrates  a  curious  chapter  in  the  his- 
tory of  the  meteor  swarm  that  has  been  worked  out  by 
mathematical  analysis,  and  is  probably  a  pretty  good  ac- 
count of  what  actually  befell  them.  Early  in  the  second 
century  of  the  Christian  era  this  flock  of  meteors  came 
down  toward  the  sun  from  outer  space,  moving  along  a 
parabolic  orbit  which  would  have  carried  it  just  inside  the 
orbit  of  Jupiter,  and  then  have  sent  it  off  to  return  no 
more.  But  such  was  not  to  be  its  fate.  As  it  approached 
the  orbit  of  Uranus,  in  the  year  126  A.  D.,  that  planet 
chanced  to  be  very  near  at  hand  and  perturbed  the  motion 
of  the  meteors  to  such  an  extent  that  the  character  of  their 
orbit  was  completely  changed  into  the  ellipse  shown  in  the 
figure,  and  in  this  new  orbit  they  have  moved  from  that 
time  to  this,  permanent  instead  of  transient  members  of 
the  solar  system.  The  perturbations,  however,  did  not  end 
with  the  year  in  which  the  meteors  were  captured  and  an- 
nexed to  the  solar  system,  but  ever  since  that  time  Jupiter, 
Saturn,  and  Uranus  have  been  pulling  together  upon  the 
orbit,  and  have  gradually  turned  it  around  into  its  present 
position  as  shown  in  the  figure,  and  it  is  chiefly  this  shift- 
ing of  the  orbit's  position  in  the  thousand  years  that  have 
elapsed  since  902  A.  D.  that  makes  the  meteor  shower  now 
come  in  November  instead  of  in  October  as  it  did  then. 


276  ASTRONOMY 

174.  Breaking  up  a  meteor  swarm,— How  closely  packed 
together  these  meteors  were  at  the  time  of  their  annexation 
to  the  solar  system  is  unknown,  but  it  is  certain  that  ever 
since  that  time  the  sun  has  been  exerting  upon  them  a 
tidal  influence  tending  to  break  up  the  swarm  and  distribute 
its  particles  around  the  orbit,  as  the  Perseids  are  distrib- 
uted, and,  given  sufficient  time,  it  will  accomplish  this,  but 
up  to  the  present  the  work  is  only  partly  done.     A  certain 
number  of  the  meteors  have  gained  so  much  over  the  slower 
moving  ones  as  to  have  made  an  extra  circuit  of  the  orbit 
and  overtaken  the  rear  of  the  procession,  so  that  there  is  a 
thin  stream  of  them  extending  entirely  around  the  orbit 
and  furnishing  in  every  November  a  Leonid  shower;  but  by 
far  the  larger  part  of  the  meteors  still  cling  together,  al- 
though drawn  out  into  a  stream  or  ribbon,  which,  though 
very  thin,  is  so  long  that  it  takes  some  three  years  to  pass 
through  the  perihelion  of  its  orbit.     It  is  only  when  the 
earth  plunges  through  this  ribbon,  as  it  should  in  1899, 
1900,  1901,  that  brilliant  Leonid  showers  can  be  expected. 

175.  Relation  of  comets  and  meteors. — It  appears  from 
the  foregoing  that  meteors  and  comets  move  in  similar  or- 
bits, and  we  have  now  to  push  the  analogy  a  little  further 
and  note  that  in  some,  instances  at  least  they  move  in  iden- 
tically the  same  orbit,  or  at  least  in  orbits  so  like  that  an 
appreciable  difference  between  them  is  hardly  to  be  found. 
Thus  a  comet  which  was  discovered  and  observed  early  in 
the  year  1866,  moves  in  the  same  orbit  with  the  Leonid 
meteors,  passing  its  perihelion  about  ten  months  ahead  of 
the  main  body  of  the  meteors.     If  it  were  set  back  in  its 
orbit  by  ten  months'  motion,  it  would  be  a  part  of  the  meteor 
swarm.    Similarly,  the  Perseid  meteors  have  a  comet  moving 
in  their  orbit  actually  immersed   in  the  stream  of  meteor 
particles,  and  several  other  of  the  more  conspicuous  star 
showers  have  comets  attending  them. 

Perhaps  the  most  remarkable  case  of  this  character  is 
that  of  a  shower  which  comes  in  the  latter  part  of  Govern- 


COMETS  AND  METEORS  27Y 

ber  from  the  constellation  Andromeda,  and  which  from  its 
association  with  the  comet  called  Biela  (after  the  name  of 
its  discoverer)  is  frequently  referred  to  as  the  Bielid  shower. 
This  comet,  an  inconspicuous  one  moving  in  an  unusually 
small  elliptical  orbit,  had  been  observed  at  various  times 
from  1772  down  to  1846  without  presenting  anything  re- 
markable in  its  appearance;  but  about  the  beginning  of  the 
latter  year,  with  very  little  warning,  it  broke  in  two,  and 
for  three  months  the  pieces  were  watched  by  astronomers 
moving  off,  side  by  side,  something  more  than  half  as  far 
apart  as  are  the  earth  and  moon.  It  disappeared,  made  the 
circuit  of  its  orbit,  and  six  years  later  came  back,  with  the 
fragments  nearly  ten  times  as  far  apart  as  before,  and  after 
a  short  stay  near  the  earth  once  more  disappeared  in  the  dis- 
tance, never  to  be  seen  again,  although  the  fragments  should 
have  returned  to  perihelion  at  least  half  a  dozen  times  since 
then.  In  one  respect  the  orbit  of  the  comet  was  remark- 
able :  it  passed  through  the  place  in  which  the  earth  stands 
on  November  27th  of  each  year,  so  that  if  the  comet  were  at 
that  particular  part  of  its  orbit  on  any  November  27th,  a 
collision  between  it  and  the  earth  would  be  inevitable.  So 
far  as  is  known,  no  such  collision  with  the  comet  has  ever 
occurred,  but  the  Bielid  meteors  which  are  strung  along 
its  orbit  do  encounter  the  earth  on  that  date,  in  greater  or 
less  abundance  in  different  years,  and  are  watched  with 
much  interest  by  the  astronomers  who  look  upon  them  as 
the  final  appearance  of  the  debris  of  a  worn-out  comet. 

176.  Periodic  comets, — The  Biela  comet  is  a  specimen  of 
the  type  which  astronomers  call  periodic  comets — i.  e., 
those  which  move  in  small  ellipses  and  have  correspond- 
ingly short  periodic  times,  so  that  they  return  frequently 
and  regularly  to  perihelion.  The  comets  which  accompany 
the  other  meteor  swarms — Leonids,  Perseids,  etc. — also  be- 
long to  this  class  as  do  some  30  or  40  others  which  have 
periodic  times  less  than  a  century.  As  has  been  already 
indicated,  these  deviations  from  the  normal  parabolic  orbit 


2Y8  ASTRONOMY 

call  for  some  special  explanation,  and  the  substance  of  that 
explanation  is  contained  in  the  account  of  the  Leonid 
meteors  and  their  capture  by  Uranus.  Any  comet  may  be 
thus  captured  by  the  attraction  of  a  planet  near  which  it 
passes.  It  is  only  necessary  that  the  perturbing  action 
of  the  planet  should  result  in  a  diminution  of  the  comet's 
velocity,  for  we  have  already  learned  that  it  is  this  velocity 
which  determines  the  character  of  the  orbit,  and  anything 
less  than  the  velocity  appropriate  to  a  parabola  must  pro- 
duce an  ellipse — i.  e.,  a  closed  orbit  around  which  the  body 
will  revolve  time  after  time  in  endless  succession.  We 
note  in  Fig.  115  that  when  the  Leonid  swarm  encountered 
Uranus  it  passed  in  front  of  the  planet  and  had  its  velocity 
diminished  and  its  orbit  changed  into  an  ellipse  thereby. 
It  might  have  passed  behind  Uranus,  it  would  have  passed 
behind  had  it  come  a  little  later,  and  the  effect  would  then 
have  been  just  the  opposite.  Its  velocity  would  have  been 
increased,  its  orbit  changed  to  a  hyperbola,  and  it  would 
have  left  the  solar  system  more  rapidly  than  it  came  into 
it,  thrust  out  instead  of  held  in  by  the  disturbing  planet. 
Of  such  cases  we  can  expect  no  record  to  remain,  but  the 
captured  comet  is  its  own  witness  to  what  has  happened, 
and  bears  imprinted  upon  its  orbit  the  brand  of  the  planet 
which  slowed  down  its  motion.  Thus  in  Fig.  115  the  changed 
orbit  of  the  meteors  has  its  aphelion  (part  remotest  from 
the  sun)  quite  close  to  the  orbit  of  Uranus,  and  one  of  its 
nodes,  y,  the  point  in  which  it  cuts  through  the  plane  of 
the  ecliptic  from  north  to  south  side,  is  also  very  near  to 
the  same  orbit.  It  is  these  two  marks,  aphelion  and  node, 
which  by  their  position  identify  Uranus  as  the  planet  in- 
strumental in  capturing  the  meteor  swarm,  and  the  date  of 
the  capture  is  found  by  working  back  with  their  respective 
periodic  times  to  an  epoch  at  which  planet  and  comet  were 
simultaneously  near  this  node. 

Jupiter,  by  reason  of  his  great  mass,  is  an  especially  effi- 
cient capturer  of  comets,  and  Fig.  116  shows  his  group  of 


COMETS  AND  METEORS  279 

captives,  his  family  of  comets  as  they  are  sometimes  called. 
The  several  orbits  are  marked  with  the  names  commonly 
given  to  the  comets.  Frequently  this  is  the  name  of  their 
discoverer,  but  often  a  different  system  is  followed — e.  g., 


FIG.  116.— Jupiter's  family  of  comets. 

the  name  1886,  IV,  means  the  fourth  comet  to  pass  through 
perihelion  in  the  year  1886.  The  other  great  planets — 
Saturn,  Uranus,  Neptune — have  also  their  families  of  cap- 
tured comets,  and  according  to  Schulhof,  who  does  not 
entirely  agree  with  the  common  opinion  about  captured 
comets,  the  earth  has  caught  no  less  than  nine  of  these 
bodies. 

1 77.  Comet  groups. — But  there  is  another  kind  of  comet 
family,  or  comet  group  as  it  is  called,  which  deserves  some 
notice,  and  which  is  best  exemplified  by  the  Great  Comet  of 
1882  and  its  relatives.  No  less  than  four  other  comets  are 
known  to  be  traveling  in  substantially  the  same  orbit  with 


280  ASTRONOMY 

this  one,  the  group  consisting  of  comets  1668,  I ;  1843,  I ; 
1880,  I ;  1882,  II ;  1887,  I.  The  orbit  itself  is  not  quite  a 
parabola,  but  a  very  elongated  ellipse,  whose  major  axis 
and  corresponding  periodic  time  can  not  be  very  accu- 
rately determined  from  the  available  data,  but  it  certainly 
extends  far  beyond  the  orbit  of  Neptune,  and  requires  not 
less  than  500  years  for  the  comet  to  complete  a  revolution 
in  it.  It  was  for  a  time  supposed  that  some  one  of  the 
recent  comets  of  this  group  of  five  might  be  a  return  of 
the  comet  of  1668  brought  back  ahead  of  time  by  unknown 
perturbations.  There  is  still  a  possibility  of  this,  but  it  is 
quite  out  of  the  question  to  suppose  that  the  last  four 
members  of  the  group  are  anything  other  than  separate 
and  distinct  comets  moving  in  practically  the  same  orbit. 
This  common  orbit  suggests  a  common  origin  for  the 
comets,  but  leaves  us  to  conjecture  how  they  became  sep- 
arated. 

The  observed  orbits  of  these  five  comets  present  some 
slight  discordances  among  themselves,  but  if  we  suppose 
each  comet  to  move  in  the  average  of  the  observed  paths  it 
is  a  simple  matter  to  fix  their  several  positions  at  the  pres- 
ent time.  They  have  all  receded  from  the  sun  nearly  on 
line  toward  the  bright  star  Sirius,  and  were  all  of  them,  at 
the  beginning  of  the  year  1900,  standing  nearly  motionless 
inside  of  a  space  not  bigger  than  the  sun  and  distant  from 
the  sun  about  150  radii  of  the  earth's  orbit.  The  great 
rapidity  with  which  they  swept  through  that  part  of  their 
orbit  near  the  sun  (see  §  162)  is  being  compensated  by 
the  present  extreme  slowness  of  their  motions,  so  that 
the  comets  of  1668  and  1882,  whose  passages  through  the 
solar  system  were  separated  by  an  interval  of  more  than 
two  centuries,  now  stand  together  near  the  aphelion  of  their 
orbits,  separated  by  a  distance  only  50  per  cent  greater  than 
the  diameter  of  the  moon's  orbit,  and  they  will  continue 
substantially  in  this  position  for  some  two  or  three  centu- 
ries to  come. 


COMETS  AND   METEORS  281 

The  slowness  with  which  these  bodies  move  when  far 
from  the  sun  is  strikingly  illustrated  by  an  equation  of 
celestial  mechanics  which  for  parabolic  orbits  takes  the 
place  of  Kepler's  Third  Law  —  viz.  : 


where  T  is  the  time,  in  years,  required  for  the  comet  to 
move  from  its  perihelion  to  any  remote  part  of  the  orbit, 
whose  distance  from  the  sun  is  represented,  in  radii  of  the 
earth's  orbit,  by  r.  If  the  comet  of  1668  had  moved  in  a 
parabola  instead  of  the  ellipse  supposed  above,  how  many 
years  would  have  been  required  to  reach  its  present  dis- 
tance from  the  sun  ? 

178.  Relation  of  comets  to  the  solar  system.  —  The  orbits 
of  these  comets  illustrate  a  tendency  which  is  becoming 
ever  more  strongly  marked.  Because  comet  orbits  are 
nearly  parabolas,  it  used  to  be  assumed  that  they  were 
exactly  parabolic,  and  this  carried  with  it  the  conclusion 
that  comets  have  their  origin  outside  the  solar  system.  It 
may  be  so,  and  this  view  is  in  some  degree  supported  by 
the  fact  that  these  nearly  parabolic  orbits  of  both  comets 
and  meteors  are  tipped  at  all  possible  angles  to  the  plane 
of  the  ecliptic  instead  of  lying  near  it  as  do  the  orbits  of 
the  planets  ;  and  by  the  further  fact  that,  unlike  the  planets, 
the  comets  show  no  marked  tendency  to  move  around  their 
orbits  in  the  direction  in  which  the  sun  rotates  upon  his 
axis.  There  is,  in  fact,  the  utmost  confusion  among  them 
in  this  respect,  some  going  one  way  and  some  another. 
The  law  of  bhe  solar  system  (gravitation)  is  impressed  upon 
their  movements,  but  its  order  is  not. 

But  as  observations  grow  more  numerous  and  more 
precise,  and  comet  orbits  are  determined  with  increasing 
accuracy,  there  is  a  steady  gain  in  the  number  of  elliptic 
orbits  at  the  expense  of  the  parabolic  ones,  and  if  comets 
are  of  extraneous  origin  we  must  admit  that  a  very  con- 
19 


282  ASTRONOMY 

siderable  percentage  of  them  have  their  velocities  slowed 
down  within  the  solar  system,  perhaps  not  so  much  by  the 
attraction  of  the  planets  as  by  the  resistance  offered  to  their 
motion  by  meteor  particles  and  swarms  along  their  paths. 
A  striking  instance  of  what  may  befall  a  comet  in  this  way 
is  shown  in  Fig.  117,  where  the  tail  of  a  comet  appears 


FIG.  117.—  Brooks's  comet,  October  21,  1893.— BARNARD. 

sadly  distorted  and  broken  by  what  is  presumed  to  have 
been  a  collision  with  a  meteor  swarm.  A  more  famous  case 
of  impeded  motion  is  oifered  by  the  comet  which  bears  the 
name  of  Encke.  This  has  a  periodic  time  less  than  that  of 
any  other  known  comet,  and  at  intervals  of  forty  months 
comes  back  to  perihelion,  each  time  moving  in  a  little 
smaller  orbit  than  before,  unquestionably  on  account  of 
some  resistance  which  it  has  suffered. 

179.  The  development  of  a  comet, — "We  saw  in  §  174 
that  the  sun's  action  upon  a  meteor  swarm  tends  to 
break  it  up  into  a  long  stream,  and  the  same  tendency  to 


COMETS  AND  METEORS  283 

break  up  is  true  of  comets  whose  attenuated  substance  pre- 
sents scant  resistance  to  this  force.  According  to  the 
mathematical  analysis  of  Eoche,  if  the  comet  stood  still 
the  sun's  tidal  force  would  tend  first  to  draw  it  out  on  line 
with  the  sun,  just  as  the  earth's  tidal  force  pulled  the- 
moon  out  of  shape  (§  42),  and  then  it  would  cause  the 
lighter  part  of  the  comet's  substance  to  flow  away  from 
both  ends  of  this  long  diameter.  This  destructive  action 
of  the  sun  is  not  limited  to  comets  and  meteor  streams, 
for  it  tends  to  tear  the  earth  and  moon  to  pieces  as  well ; 
but  the  densities  and  the  resulting  mutual  attractions  of 
their  parts  are  far  too  great  to  permit  this  to  be  accom- 
plished. 

As  a  curiosity  of  mathematical  analysis  we  may  note 
that  a  spherical  cloud  of  meteors,  or  dust  particles  weigh- 
ing a  gramme  each,  and  placed  at  the  earth's  distance  from 
the  sun,  will  be  broken  up  and  dissipated  by  the  sun's  tidal 
action  if  the  average  distance  between  the  particles  exceeds 
two  yards.  Now,  the  earth  is  far  more  dense  than  such  a 
cloud,  whose  extreme  tenuity,  however,  suggests  what  we 
have  already  learned  of  the  small  density  of  comets,  and 
prepares  us  in  their  case  for  an  outflow  of  particles  at  both 
ends  of  the  diameter  directed  toward  the  sun.  Some- 
thing of  this  kind  actually  occurs,  for  the  tail  of  a  comet 
streams  out  on  the  side  opposite  to  the  sun,  and  in  general 
points  away  from  the  sun,  as  is  shown  in  Fig.  109,  and  the 
envelopes  and  jets  rise  up  toward  the  sun ;  but  an  inspec- 
tion of  Fig.  106  will  show  that  the  tail  and  the  envelope 
are  too  unlike  to  be  produced  by  one  and  the  same  set  of 
forces. 

It  was  long  ago  suggested  that  the  sun  possibly  exerts 
upon  a  comet's  substance  a  repelling  force  in  addition  to 
the  attracting  force  which  we  call  gravity.  We  think  nat- 
urally in  this  connection  of  the  repelling  force  which  a 
charge  of  electricity  exerts  upon  a  similar  charge  placed 
on  a  neighboring  body,  and  we  note  that  if  both  sun  and 


284  ASTRONOMY 

comet  carried  a  considerable  store  of  electricity  upon  their 
surfaces  this  would  furnish  just  such  a  repelling  force  as 
seems  indicated  by  the  phenomena  of  comets'  tails  ;  for  the 
force  of  gravity  would  operate  between  the  substance  of 
sun  and  comet,  and  on  the  whole  would  be  the  controlling 
force,  while  the  electric  charges  would  produce  a  repulsion, 
relatively  feeble  for  the  big  particles  and  strong  for  the 
little  ones,  since  an  electric  charge  lies  wholly  on  the  sur- 
face, while  gravity  permeates  the  whole  mass  of  a  body, 
and  the  ratio  of  volume  (gravity)  to  surface  (electric 
charge)  increases  rapidly  with  increasing  size.  The  repel- 
ling force  would  thrust  back  toward  the  comet  those  parti- 
cles which  flowed  out  toward  the  sun,  while  it  would  urge 
forward  those  which  flowed  away  from  it,  thus  producing 
the  difference  in  appearance  between  tail  and  envelopes, 
the  latter  being  regarded  from  this  standpoint  as  stunted 
tails  strongly  curved  backward.  In  recent  years  the  Eus- 
sian  astronomer  Bredichin  has  made  a  careful  study  of  the 
shape  and  positions  of  comets'  tails  and  finds  that  they  fit 
with  mathematical  precision  to  the  theories  of  electric 
repulsion. 

180.  Comet  tails. — According  to  Bredichin,  a  comet's 
tail  is  formed  by  something  like  the  following  process  :  In 
the  head  of  the  comet  itself  a  certain  part  of  its  matter  is 
broken  up  into  fine  bits,  single  molecules  perhaps,  which, 
as  they  no  longer  cling  together,  may  be  described  as  in 
the  condition  of  vapor.  By  the  repellent  action  of  both 
sun  and  comet  these  molecules  are  cast  out  from  the  head 
of  the  comet  and  stream  away  in  the  direction  opposite  to 
the  sun  with  different  velocities,  the  heavy  ones  slowly  and 
the  light  ones  faster,  much  as  particles  of  smoke  stream 
away  from  a  smokestack,  making  for  the  comet  a  tail 
which  like  a  trail  of  smoke  is  composed  of  constantly 
changing  particles.  The  result  of  this  process  is  shown 
in  Fig.  118,  where  the  positions  of  the  comet  in  its  orbit 
on  successive  days  are  marked  by  the  Roman  numerals,  and 


COMETS  AND  METEORS 


285 


the  broken  lines  represent  the  paths  of  molecules  m1,  m11, 
mm,  etc.,  expelled  from  it  on  their  several  dates  and  travel- 
ing thereafter  in 
orbits  determined 
by  the  combined 
effect  of  the  sun's 
attraction,  the 
sun's  repulsion, 
and  the  comet's 
repulsion.  The 
comet's  attrac- 
tion (gravity)  is 
too  small  to  be 
taken  into  ac- 
count. The  line 
drawn  upward 
from  VI  repre- 
sents the  posi- 
tions of  these 
molecules  on  the 
sixth  day,  and 
shows  that  all  of 
them  are  arranged 
in  a  tail  pointing 

nearly  away  from  the  sun.  A  similar  construction  for  the 
other  dates  gives  the  corresponding  positions  of  the  tail, 
always  pointing  away  from  the  sun. 

Only  the  lightest  kind  of  molecules — e.  g.,  hydrogen — 
could  drift  away  from  the  comet  so  rapidly  as  is  here  shown. 
The  heavier  ones,  such  as  carbon  and  iron,  would  be  re- 
pelled as  strongly  by  the  electric  forces,  but  they  would  be 
more  strongly  pulled  back  by  the  gravitative  forces,  thus 
producing  a  much  slower  separation  between  them  and  the 
head  of  the  comet.  Construct  a  figure  such  as  the  above, 
in  which  the  molecules  shall  recede  from  the  comet  only 
one  eighth  as  fast  as  in  Fig.  118,  and  note  what  a  different 


FIG.  118.— Formation  of  a  comet's  tail. 


286  ASTRONOMY 

position  it  gives  to  the  comet's  tail.  Instead  of  pointing 
directly  away  from  the  sun,  it  will  be  bent  strongly  to  one 
side,  as  is  the  large  plume-shaped  tail  of  the  Donati  comet 
shown  in  Fig.  101.  But  observe  that  this  comet  has  also  a 
nearly  straight  tail,  like  the  theoretical  one  of  Fig.  118. 
We  have  here  two  distinct  types  of  comet  tails,  and  accord- 
ing to  Bredichin  there  is  still  another  but  unusual  type, 
even  more  strongly  bent  to  one  side  of  the  line  joining 
comet  and  sun,  and  appearing  quite  short  and  stubby. 
The  existence  of  these  three  types,  and  their  peculiarities 
of  shape  and  position,  are  all  satisfactorily  accounted  for 
by  the  supposition  that  they  are  made  of  different  mate- 
rials. The  relative  molecular  weights  of  hydrogen,  some  of 
the  hydrocarbons,  and  iron,  are  such  that  tails  composed 
of  these  molecules  would  behave  just  as  do  the  actual  tails 
observed  and  classified .  into  these  three  types.  The  spec- 
troscope shows  that  these  materials — hydrogen,  hydrocar- 
bons, and  iron — are  present  in  comets,  and  leaves  little 
room  for  doubt  of  the  essential  soundness  of  Bredichin's 
theory. 

181.  Disintegration  of  comets. — We  must  regard  the  tail 
as  waste  matter  cast  off  from  the  comet's  head,  and  although 
the  amount  of  this  matter  is  very  small,  it  must  in  some 
measure  diminish  the  comet's  mass.  This  process  is,  of 
course,  most  active  at  the  time  of  perihelion  passage,  and 
if  the  comet  returns  to  perihelion  time  after  time,  as  the 
periodic  ones  which  move  in  elliptic  orbits  must  do,  this 
waste  of  material  may  become  a  serious  matter,  leading 
ultimately  to  the  comet's  destruction.  It  is  significant  in 
this  connection  that  the  periodic  comets  are  all  small  and 
inconspicuous,  not  one  of  them  showing  a  tail  of  any  con- 
siderable dimensions,  and  it  appears  probable  that  they  are 
far  advanced  along  the  road  which,  in  the  case  of  Biela's 
comet,  led  to  its  disintegration.  Their  fragments  are  in 
part  strewn  through  the  solar  system,  making  some  small 
fraction  of  its  cloud  of  cosmic  dust,  and  in  part  they  have 


COMETS  AND  METEORS  287 

been  carried  away  from  the  sun  and  scattered  throughout 
the  universe  along  hyperbolic  orbits  impressed  upon  them 
at  the  time  they  left  the  comet. 

But  it  is  not  through  the  tail  only  that  the  disinte- 
grating process  is  worked  out.  While  Biela's  comet  is  per- 
haps the  most  striking  instance  in  which  the  head  has 
broken  up,  it  is  by  no  means  the  only  one.  The  Great 
Comet  of  1882  cast  off  a  considerable  number  of  fragments 
which  moved  away  as  independent  though  small  comets 
and  other  more  recent  comets  have  been  seen  to  do  the 
same.  An  even  more  striking  phenomenon  was  the  grad- 
ual breaking  up  of  the  nucleus  of  the  same  comet,  1882, 
II,  into  a  half  dozen  nuclei  arranged  in  line  like  beads 
upon  a  string,  and  pointing  along  the  axis  of  the  tail.  See 
Fig.  119,  which  shows  the  series  of  changes  observed  in 
the  head  of  this  comet. 

182.  Comets  and  the  spectroscope. — The  spectrum  pre- 
sented by  comets  was  long  a  puzzle,  and  still  retains  some- 
thing of  that  character,  although  much  progress  has  been 
made  toward  an  understanding  of  it.  In  general  it  con- 
sists of  two  quite  distinct  parts — first,  a  faint  background 
of  continuous  spectrum  due  to  ordinary  sunlight  reflected 
from  the  comet ;  and,  second,  superposed  upon  this,  three 
bright  bands  like  the  carbon  band  shown  at  the  middle  of 
Fig.  48,  only  not  so  sharply  defined.  These  bands  make  a 
discontinuous  spectrum  quite  similar  to  that  given  off  by 
compounds  of  hydrogen  and  carbon,  and  of  course  indicate 
that  a  part  of  the  comet's  light  originates  in  the  body 
itself,  which  must  therefore  be  incandescent,  or  at  least 
must  contain  some  incandescent  portions. 

By  heating  hydrocarbons  in  our  laboratories  until  they 
become  incandescent,  something  like  the  comet  spectrum 
may  be  artificially  produced,  but  the  best  approximation 
to  it  is  obtained  by  passing  a  disruptive  electrical  dis- 
charge through  a  tube  in  which  fragments  of  meteors 
have  been  placed.  A  flash  of  lightning  is  a  disruptive 


October  9,  1882. 


November  21,  1882. 


February  1,  1883.  March  3,  1883. 

FIG.  119.— The  head  of  the  Great  Comet  of  1882.— WINLOCK. 


COMETS  AND   METEORS  289 

electrical  discharge  upon  a  grand  scale.  Now,  meteors 
and  electric  phenomena  have  been  independently  brought 
to  our  notice  in  connection  with  comets,  and  with  this 
suggestion  it  is  easy  to  frame  a  general  idea  of  the  phys- 
ical condition  of  these  objects — for  example,  a  cloud  of 
meteors  of  different  sizes  so  loosely  clustered  that  the 
average  density  of  the  swarm  is  very  low  indeed  ;  the  sev- 
eral particles  in  motion  relative  to  each  other,  as  well  as  to 
the  sun,  and  disturbed  in  that  motion  by  the  sun's  tidal 
action.  Each  particle  carries  its  own  electric  charge, 
which  may  be  of  higher  or  lower  tension  than  that  of  its 
neighbor,  and  is  ready  to  leap  across  the  intervening  gap 
whenever  two  particles  approach  each  other.  To  these 
conditions  add  the  inductive  effect  of  the  sun's  electric 
charge,  which  tends  to  produce  a  particular  and  artificial 
distribution  of  electricity  among  the  comet's  particles,  and 
we  may  expect  to  find  an  endless  succession  of  sparks,  tiny 
lightning  flashes,  springing  from  one  particle  to  another, 
most  frequent  and  most  vivid  when  the  comet  is  near  the 
sun,  but  never  strong  enough  to  be  separately  visible. 
Their  number  is,  however,  great  enough  to  make  the  comet 
in  part  self-luminous  with  three  kinds  of  light — i.  e.,  the  three 
bright  bands  of  its  spectrum,  whose  wave  lengths  show  in 
the  comet  the  same  elements  and  compounds  of  the  ele- 
ments— carbon,  hydrogen,  and  oxygen — which  chemical 
analysis  finds  in  the  fallen  meteor.  It  is  not  to  be  sup- 
posed that  these  are  the  only  chemical  elements  in  the 
comet,  as  they  certainly  are  not  the  only  ones  in  the  me- 
teor. They  are  the  easy  ones  to  detect  under  ordinary  cir- 
cumstances, but  in  special  cases,  like  that  of  the  Great 
Comet  of  1882,  whose  near  approach  to  the  sun  rendered 
its  whole  substance  incandescent,  the  spectrum  glows  with 
additional  bright  lines  of  sodium,  iron,  etc. 

183.  Collisions. — A  question  sometimes  asked,  What 
would  be  the  effect  of  a  collision  between  the  earth  and  a 
comet  ?  finds  its  answer  in  the  results  reached  in  the  pre- 


290  ASTRONOMY 

ceding  sections.  There  would  be  a  star  shower,  more  or 
less  brilliant  according  to  the  number  and  size  of  the  pieces 
which  made  up  the  comet's  head.  If  these  were  like  the 
remains  of  the  Biela  comet,  the  shower  might  even  be  a 
very  tame  one ;  but  a  collision  with  a  great  comet  would 
certainly  produce  a  brilliant  meteoric  display  if  its  head 
came  in  contact  with  the  earth.  If  the  comet  were  built  of 
small  pieces  whose  individual  weights  did  not  exceed  a  few 
ounces  or  pounds,  the  earth's  atmosphere  would  prove  a 
perfect  shield  against  their  attacks,  reducing  the  pieces  to 
harmless  dust  before  they  could  reach  the  ground,  and 
leaving  the  earth  uninjured  by  the  encounter,  although  the 
comet  might  suffer  sadly  from  it.  But  big  stones  in  the 
comet,  meteors  too  massive  to  be  consumed  in  their  flight 
through  the  air,  might  work  a  very  different  effect,  and  by 
their  bombardment  play  sad  havoc  with  parts  of  the  earth's 
surface,  although  any  such  result  as  the  wrecking  of  the 
earth,  or  the  destruction  of  all  life  upon  it,  does  not  seem 
probable.  The  40  meteors  of  §  169  may  stand  for  a  colli- 
sion with  a  small  comet.  Consult  the  Bible  (Joshua  x,  11) 
for  an  example  of  what  might  happen  with  a  larger  one. 


CHAPTEE  XIII 

THE    FIXED    STARS 

184.  The  constellations. — In  the  earlier  chapters  the  stu- 
dent has  learned  to  distinguish  between  wandering  stars 
(planets)  and  those  fixed  luminaries  which  remain  year  after 
year  in  the  same  constellation,  shining  for  the  most  part 
with  unvarying  brilliancy,  and  presenting  the  most  perfect 
known  image  of  immutability.  Homer  and  Job  and  pre- 
historic man  saw  Orion  and  the  Pleiades  much  as  we  see 
them  to-day,  although  the  precession,  by  changing  their 
relation  to  the  pole  of  the  heavens,  has  altered  their  risings 
and  settings,  and  it  may  be  that  their  luster  has  changed 
in  some  degree  as  they  grew  old  with  the  passing  centuries. 

The  division  of  the  sky  into  constellations  dates  back  to 
the  most  primitive  times,  long  before  the  Christian  era, 
and  the  crooked  and  irregular  boundaries  of  these  con- 
stellations as  shown  by  the  dotted  lines  in  Fig.  120,  such 
as  no  modern  astronomer  would  devise,  are  an  inher- 
itance from  antiquity,  confounded  and  made  worse  in  its 
descent  to  our  day.  The  boundaries  assigned  to  constella- 
tions near  the  south  pole  are  much  more  smooth  and  regu- 
lar, since  this  part  of  the  sky,  invisible  to  the  peoples  from 
whom  we  inherit,  was  not  studied  and  mapped  until  more 
modern  times.  The  old  traditions  associated  with  each 
constellation  a  figure,  often  drawn  from  classical  mythol- 
ogy, which  was  supposed  to  be  suggested  by  the  grouping 
of  the  stars  :  thus  Ursa  Major  is  a  great  bear,  stalking  across 
the  sky,  with  the  handle  of  the  Dipper  for  his  tail ;  Leo  is  a 
lion  ;  Cassiopeia,  a  lady  in  a  chair ;  Andromeda,  a  maiden 

291 


THE   FIXED  STARS  293 

chained  to  a  rock,  etc. ;  but  for  the  most  part  the  resem- 
blances are  far-fetched  and  quite  too  fanciful  to  be  followed 
by  the  ordinary  eye. 

185.  The  number  of  stars. — "  As  numerous  as  the  stars 
of  heaven  "  is  a  familiar  figure  of  speech  for  expressing  the 
idea  of   countless  number,  but  as  applied  to   the  visible 
stars  of  the  sky  the  words  convey  quite  a  wrong  impression, 
for,  under  ordinary  circumstances,  in  a  clear  sky  every  star 
to  be  seen  may  be  counted  in  the  course  of  a  few  hours, 
since  they  do  not  exceed  3,000  or  4,000,  the  exact  number 
depending  upon  atmospheric  conditions  and  the  keenness 
of  the  individual  eye.     Test  your  own  vision  by  counting 
the  stars  of  the  Pleiades.     Six  are  easily  seen,  and  you  may 
possibly  find  as  many  as  ten  or  twelve ;  but  however  many 
are  seen,  there  will  be  a  vague  impression  of  more  just  be- 
yond the  limit  of  visibility,  and  doubtless  this  impression  is 
partly  responsible  for  the  popular  exaggeration  of  the  num- 
ber of  the  stars.     In  fact,  much  more  than  half  of  what  we 
call  starlight  comes  from  stars  which  are  separately  too 
small  to  be  seen,  but  whose  number  is  so  great  as  to  more 
than  make  up  for  their  individual  faintness. 

The  Milky  Way  is  just  such  a  cloud  of  faint  stars,  and 
the  student  who  can  obtain  access  to  a  small  telescope,  or 
even  an  opera  glass,  should  not  fail  to  turn  it  toward  the 
Milky  Way  and  see  for  himself  how  that  vague  stream  of 
light  breaks  up  into  shining  points,  each  an  independent 
star.  These  faint  stars,  which  are  found  in  every  part  of 
the  sky  as  well  as  in  the  Milky  Way,  are  usually  called 
telescopic,  in  recognition  of  the  fact  that  they  can  be  seen 
only  in  the  telescope,  while  the  other  brighter  ones  are 
known  as  lucid  stars. 

186.  Magnitudes, — The  telescopic  stars  show  among  them- 
selves an  even  greater  range  of  brightness  than  do  the  lucid 
ones,  and  the  system  of  magnitudes  (§  9)  has  accordingly 
been  extended  to  include  them,  the  faintest  star  visible  in 
the  greatest  telescope  of  the  present  time  being  of  the  six- 


294  ASTRONOMY 

teenth  or  seventeenth  magnitude,  while,  as  we  have  already 
learned,  stars  on  the  dividing  line  between  the  telescopic  and 
the  lucid  ones  are  of  the  sixth  magnitude.  To  compare  the 
amount  of  light  received  from  the  stars  with  that  from  the 
planets,  and  particularly  from  the  sun  and  moon,  it  has 
been  found  necessary  to  prolong  the  scale  of  magnitudes 
backward  into  the  negative  numbers,  and  we  speak  of  the 
sun  as  having  a  stellar  magnitude  represented  by  the  num- 
ber —26.5.  The  full  moon's  stellar  magnitude  is  —  12,  and 
the  planets  range  from  —  3  (Venus)  to  -f-  8  (Neptune). 
Even  a  very  few  of  the  stars  are  so  bright  that  negative 
magnitudes  must  be  used  to  represent  their  true  relation 
to  the  fainter  ones.  Sirius,  for  example,  the  brightest  of 
the  fixed  stars,  is  of  the  —  1  magnitude,  and  such  stars  as 
Arcturus  and  Vega  are  of  the  0  magnitude. 

The  relation  of  these  magnitudes  to  each  other  has  been 
so  chosen  that  a  star  of  any  one  magnitude  is  very  approxi- 
mately 2.5  times  as  bright  as  one  of  the  next  fainter  mag- 
nitude, and  this  ratio  furnishes  a  convenient  method  of 
comparing  the  amount  of  light  received  from  different  stars. 
Thus  the  brightness  of  Venus  is  2.5  X  2-5  times  that  of 
Sirius.  The  full  moon  is  (2.5)9  times  as  bright  as  Venus, 
etc. ;  only  it  should  be  observed  that  the  number  2.5  is  not 
exactly  the  value  of  the  light  ratio  between  two  consecutive 
magnitudes.  Strictly  this  ratio  is  the  \/  100  =  2.5119-f-, 
so  that  to  be  entirely  accurate  we  must  say  that  a  difference 
of  five  magnitudes  gives  a  hundredfold  difference  of  bright- 
ness. In  mathematical  symbols,  if  B  represents  the  ratio  of 
brightness  (quantity  of  light)  of  two  stars  whose  magni- 
tudes are  m  and  n,  then 

B  =  (100)  '"?L 

How  much  brighter  is  an  ordinary  first-magnitude  star, 
such  as  Aldebaran  or  Spica,  than  a  star  just  visible  to  the 
naked  eye  ?  How  many  of  the  faintest  stars  visible  in  a 
great  telescope  would  be  required  to  make  one  star  just 


THE  FIXED  STARS  295 

visible  to  the  unaided  eye  ?  How  many  full  moons  must 
be  put  in  the  sky  in  order  to  give  an  illumination  as  bright 
as  daylight  ?  How  large  a  part  of  the  visible  hemisphere 
would  they  occupy  ? 

187.  Classification  by  magnitudes. — The  brightness  of  all 
the  lucid  stars  has  been  carefully  measured  with  an  instru- 
ment (photometer)  designed  for  that  special  purpose,  and 
the  following  table  shows,  according  to  the  Harvard  Pho- 
tometry, the  number  of  stars  in  the  whole  sky,  from  pole  to 
pole,  which  are  brighter  than  the  several  magnitudes 
named  in  the  table  : 

The  number  of  stars  brighter  than  magnitude  1.0  is      11 

2.0  "      39 

"  "  "  "  3.0  "     142 

"  "  "  ««  "  4.0  "     463 

"  "  "  "  "  5.0  "  1,483 

6.0  "  4,326 

It  must  not  be  inferred  from  this  table  that  there  are 
in  the  whole  sky  only  4,326  stars  visible  to  the  naked  eye. 
The  actual  number  is  probably  50  or  60  per  cent  greater 
than  this,  and  the  normal  human  eye  sees  stars  as  faint  as 
the  magnitude  6.4  or  6.5,  the  discordance  between  this  num- 
ber and  the  previous  statement,  that  the  sixth  magnitude  is 
the  limit  of  the  naked-eye  vision,  having  been  introduced 
in  the  attempt  to  make  precise  and  accurate  a  classification 
into  magnitudes  which  was  at  first  only  rough  and  approxi- 
mate. This  same  striving  after  accuracy  leads  to  the  intro- 
duction of  fractional  numbers  to  represent  gradations  of 
brightness  intermediate  between  whole  magnitudes.  Thus 
of  the  2,843  stars  included  between  the  fifth  and  sixth 
magnitudes  a  certain  proportion  are  said  to  be  of  the  5.1 
magnitude,  5.2  magnitude,  and  so  on  to  the  5.9  magnitude, 
even  hundredths  of  a  magnitude  being  sometimes  employed. 

We  have  found  the  number  of  stars  included  between 
the  fifth  and  sixth  magnitudes  by  subtracting  from  the 
last  number  of  the  preceding  table  the  number  immedi- 


296  ASTRONOMY 

ately  preceding  it,  and  similarly  we  may  find  the  number 
included  between  each  other  pair  of  consecutive  magni- 
tudes, as  follows : 

Magnitude 01234  5  6 

Number  of  stars. ...        11      28      103      321      1,020      2,843 
4  x  3m 12      36      108      324        972      2,916 

In  the  last  line  each  number  after  the  first  is  found  by 
multiplying  the  preceding  one  by  3,  and  the  approximate 
agreement  of  each  such  number  with  that  printed  above  it 
shows  that  on  the  whole,  as  far  as  the  table  goes,  the  fainter 
stars  are  approximately  three  times  as  numerous  as  those 
a  magnitude  brighter. 

The  magnitudes  of  the  telescopic  stars  have  not  yet 
been  measured  completely,  and  their  exact  number  is  un- 
known ;  but  if  we  apply  our  principle  of  a  threefold  increase 
for  each  successive  magnitude,  we  shall  find  for  the  fainter 
stars — those  of  the  tenth  and  twelfth  magnitudes — prodi- 
gious numbers  which  run  up  into  the  millions,  and  even  these 
are  probably  too  small,  since  down  to  the  ninth  or  tenth 
magnitude  it  is  certain  that  the  number  of  the  telescopic 
stars  increases  from  magnitude  to  magnitude  in  more  than 
a  threefold  ratio.  This  is  balanced  in  some  degree  by  the 
less  rapid  increase  which  is  known  to  exist  in  magnitudes 
still  fainter ;  and  applying  our  formula  without  regard  to 
these  variations  in  the  rate  of  increase,  we  obtain  as  a  rude 
approximation  to  the  total  number  of  stars  down  to  the 
fifteenth  magnitude,  86,000,000.  The  Herschels,  father 
and  son,  actually  counted  the  number  of  stars  visible  in 
nearly  8,000  sample  regions  of  the  sky,  and,  inferring  the 
character  of  the  whole  sky  from  these  samples,  we  find  it 
to  contain  58,500,000  stars  ;  but  the  magnitude  of  the  faint- 
est star  visible  in  their  telescope,  and  included  in  their 
count,  is  rather  uncertain. 

How  many  first-magnitude  stars  would  be  needed  to 
give  as  much  light  as  do  the  2,843  stars  of  magnitude  5.0 


THE  FIXED  STARS  297 

to  6.0  ?  How  many  tenth-magnitude  stars  are  required  to 
give  the  same  amount  of  light  ? 

To  the  modern  man  it  seems  natural  to  ascribe  the  dif- 
ferent brilliancies  of  the  stars  to  their  different  distances 
from  us ;  but  such  was  not  the  case  2,000  years  ago,  when 
each  fixed  star  was  commonly  thought  to  be  fastened  to 
a  "  crystal  sphere,"  which  carried  them  with  it,  all  at  the 
same  distance  from  us,  as  it  turned  about  the  earth.  In 
breaking  away  from  this  erroneous  idea  and  learning  to 
think  of  the  sky  itself  as  only  an  atmospheric  illusion 
through  which  we  look  to  stars  at  very  different  distances 
beyond,  it  was  easy  to  fall  into  the  opposite  error  and  to 
think  of  the  stars  as  being  much  alike  one  with  another, 
and,  like  pebbles  on  the  beach,  scattered  throughout  space 
with  some  rough  degree  of  uniformity,  so  that  in  every 
direction  there  should  be  found  in  equal  measure  stars 
near  at  hand  and  stars  far  off,  each  shining  with  a  luster 
proportioned  to  its  remoteness. 

188.  Distances  of  the  stars, — Now,  in  order  to  separate 
the  true  from  the  false  in  this  last  mode  of  thinking  about 
the  stars,  we  need  some  knowledge  of  their  real  distances 
from  the  earth,  and  in  seeking  it  we  encounter  what  is 
perhaps  the  most  delicate  and  difficult  problem  in  the 
whole  range  of  observational  astronomy.  As  shown  in 
Fig.  121,  the  principles  involved  in  determining  these  dis- 
tances are  not  fundamentally  different  from  those  em- 
ployed in  determining  the  moon's  distance  from  the  earth. 
Thus,  the  ellipse  at  the  left  of  the  figure  represents  the 
earth's  orbit  and  the  position  of  the  earth  at  different 
times  of  the  year.  The  direction  of  the  star  A  at  these 
several  times  is  shown  by  lines  drawn  through  A  and  pro- 
longed to  the  background  apparently  furnished  by  the  sky. 
A  similar  construction  is  made  for  the  star  B,  and  it  is 
readily  seen  that  owing  to  the  changing  position  of  the 
observer  as  he  moves  around  the  earth's  orbit,  both  A  and 
B  will  appear  to  move  upon  the  background  in  orbits 
20 


298  ASTRONOMY 

shaped  like  that  of  the  earth  as  seen  from  the  star,  but 
having  their  size  dependent  upon  the  star's  distance,  the 
apparent  orbit  of  A  being  larger  than  that  of  B,  because  A 
is  nearer  the  earth.  By  measuring  the  angular  distance 


July 


FIG.  121.— Determining  a  star's  parallax. 

between  A  and  B  at  opposite  seasons  of  the  year  (e.  g.,  the 
angles  A  —  Jan.  —  B,  and  A  —  July  —  B)  the  astronomer 
determines  from  the  change  in  this  angle  how  much  larger 
is  the  one  path  than  the  other,  and  thus  concludes  how 
much  nearer  is  A  than  B.  Strictly,  the  difference  between 
the  January  and  July  angles  is  equal  to  the  difference  be- 
tween the  angles  subtended  at  A  and  B  by  the  diameter  of 
the  earth's  orbit,  and  if  B  were  so  far  away  that  the  angle 
Jan.  —  B —  July  were  nothing  at  all  we  should  get  imme- 
diately from  the  observations  the  angle  Jan.  —  A — July, 
which  would  suffice  to  determine  the  stars'  distance.  Sup- 
posing the  diameter  of  the  earth's  orbit  and  the  angle  at  A 
to  be  known,  can  you  make  a  graphical  construction  that 
will  determine  the  distance  of  A  from  the  earth  ? 

The  angle  subtended  at  A  by  the  radius  of  the  earth's 
orbit — i.  e.,  -J-  (Jan.  —  A  —  July) — is  called  the  star's  paral- 
lax, and  this  is  commonly  used  by  astronomers  as  a  meas- 
ure of  the  star's  distance  instead  of  expressing  it  in  linear 
units  such  as  miles  or  radii  of  the  earth's  orbit.  The  dis- 


THE  FIXED  STARS  299 

tance  of  a  star  is  equal  to  the  radius  of  the  earth's  orbit 
divided  by  the  parallax,  in  seconds  of  arc,  and  multiplied 
by  the  number  206265. 

A  weak  point  of  this  method  of  measuring  stellar  dis- 
tances is  that  it  always  gives  what  is  called  a  relative  paral- 
lax— i.  e.,  the  difference  between  the  parallaxes  of  A  and 
B ;  and  while  it  is  customary  to  select  for  B  a  star  or  stars 
supposed  to  be  much  farther  off  than  A,  it  may  happen, 
and  sometimes  does  happen,  that  these  comparison  stars 
as  they  are  called  are  as  near  or  nearer  than  A,  and  give 
a  negative  parallax — i.  e.,  the  difference  between  the  angles 
at  A  and  B  proves  to  be  negative,  as  it  must  whenever  the 
star  B  is  nearer  than  A. 

The  first  really  successful  determinations  of  stellar 
parallax  were  made  by  Struve  and  Bessel  a  little  prior  to 
1840,  and  since  that  time  the  distances  of  perhaps  100  stars 
have  been  measured  with  some  degree  of  reliability,  al- 
though the  parallaxes  themselves  are  so  small — never  as 
great  as  1" — that  it  is  extremely  difficult  to  avoid  falling 
into  error,  since  even  for  the  nearest  star  the  problem  of 
its  distance  is  equivalent  to  finding  the  distance  of  an  ob- 
ject more  than  5  miles  away  by  looking  at  it  first  with  one 
eye  and  then  with  the  other.  Too  short  a  base  line. 

189.  The  sun  and  his  neighbors. — The  distances  of  the 
sun's  nearer  neighbors  among  the  stars  are  shown  in  Fig. 
123,  where  the  two  circles  having  the  sun  at  their  center 
represent  distances  from  it  equal  respectively  to  1,000,000 
and  2,000,000  times  the  distance  between  earth  and  sun. 
In  the  figure  the  direction  of  each  star  from  the  sun  cor- 
responds to  its  right  ascension,  as  shown  by  the  Eoman 
numerals  about  the  outer  circle ;  the  true  direction  of  the 
star  from  the  sun  can  not,  of  course,  be  shown  upon  the 
flat  surface  of  the  paper,  but  it  may  be  found  by  elevat- 
ing or  depressing  the  star  from  the  surface  of  the  paper 
through  an  angle,  as  seen  from  the  sun,  equal  to  its  declina- 
tion, as  shown  in  the  fifth  column  of  the  following  table, 


300 


ASTRONOMY 


The  Surfs  Nearest  Neighbors 


No. 

STAR. 

Magni- 
tude. 

R.  A. 

Dec. 

Parallax. 

Distance. 

1 

a  Centauri  . 

0.7 

14.  5h. 

—60° 

0  75"- 

0.27 

9 

LI.  21,185    

6.8 

11.0 

+  37 

0.45 

0  46 

8 

61  Cve-ni 

5  0 

21  0 

+  38 

0  40 

0  51 

4 

ft  Herculis          .  . 

3.6 

16.7 

+  39 

0.40 

0.51 

5 

Sirius     

—1.4 

6.7 

—  17 

0.37 

0.56 

6 

2  2  398 

8.2 

18.7 

+  59 

0.35 

0  58 

7 

Procyon  

—0.5 

7.6 

+  5 

0.34 

0.60 

8 

•y  Draconis  

4.8 

17  5 

+  55 

0.30 

0.68 

q 

Gr  34 

7.9 

0.2 

+43 

0  29 

0  71 

10 

Lac   9  352     .... 

7.5 

23.0 

—36 

0  28 

0.74 

11 
12 
18 

ff  Draconis 
A.  0.  17,415-6  .... 
i\  Cassiopeias  

4.8 
9.0 
3.4 

19.5 
17.6 
0.7 

+  69 

+  68 

+  57 

0.25 
0.25 
0.25 

0.82 
0.82 
0.82 

14 

Altair 

1  0 

19  8 

+  9 

0  21 

0.97 

15 

€  Indi 

5.2 

21.9 

—57 

0.20 

1.03 

16 

Gr.  1,618  

6.7 

10.1 

+  50 

0.20 

1.03 

17 
18 

10  Ursae  Majoris.  . 
Castor 

4.2 

1.5 

8.9 

7.5 

+  42 
+  32 

0.20 
0.20 

1.03 
1.03 

19 

LI.  21,258  

8.5 

11.0 

+  44 

0.20 

1.03 

90 

o^  Eridani 

4.5 

4.2 

—  8 

0.19 

1.08 

21 

A  0  11  677 

9  0 

11  2 

+  66 

0.19 

1.08 

22 
23 
94 

LI.  18,115  
B.  D.  36°,  3,883  .  .  . 
Gr.  1,618  

8.0 
7.1 
6.5 

9.1 
20.0 
10.1 

+  53 
+  36 
+  50 

0.18 
0.18 
0.17 

1.14 
1.14 
1.21 

9,5 

ft  Cassiopeias 

2.3 

0.1 

+  59 

0.16 

1.28 

96 

70  Ophiuchi      

4.4 

18.0 

+  2 

0.16 

1.28 

27 
98 

21,516  
Gr   1  830 

6.5 
6.6 

11.2 
11.8 

+  74 
+  39 

0.15 
0.15 

1.38 
1.38 

99 

fi  Cassiopeia) 

5.4 

1.0 

+  54 

0.14 

1.47 

30 

e  Eridani  

4.4 

3.5 

-10 

0.14 

1.47 

31 
32 

t  Qrsae  Majoris  
ft  Hydri  

3.2 
2.9 

8.9 
0.3 

+  48 

-78 

0.13 
0.13 

1.58 
1.58 

33 

Fomalhaut  

1.0 

22.9 

-30 

0.13 

1.58 

34 
35 

Br.  3,077  
e  Cvffni  .  . 

6.0 
2.5 

23.1 

20.8 

+  57 
+  33 

0.13 
0.12 

1.58 
1.71 

36 

ft  Comae  

4.5 

13.1 

+  28 

0.11 

1.87 

37 

dp  AurigaB 

8.8 

6.6 

+  44 

0.11 

1.87 

38 

if  Herculis 

3.3 

17.2 

+  37 

0.11 

1.87 

39 

Aldebaran  

1.1 

4.5 

+  16 

0.10 

2.06 

40 

Capella 

0.1 

5.1 

+  46 

0.10 

2.06 

41 
49 

B.  D.  35°,  4,003  .  .  . 
Gr.  1  646 

9.2 
6.3 

20.1 
10.3 

+  35 

+  49 

0.10 
0.10 

2.06 
2.06 

43 

y  Cysrni.  . 

2.3 

20.3 

+  40 

0.10 

2.06 

44 

Regulus 

1.2 

10.0 

+  12 

0.10 

2.06 

45 

Vega  

0.2 

18.6 

+  39 

0.10 

2.06 

THE  FIXED   STARS 


301 


in  which  the  numbers  in  the  first  column  are  those  placed 
adjacent  to  the  stars  in  the  diagram  to  identify  them. 

190.  Light  years.— The  radius  of  the  inner  circle  in  Fig. 
122,  1,000,000  times  the  earth's  distance  from  the  sun,  is  a 
convenient  unit  in  which  to  express  the  stellar  distances, 


XII 


XIII 


XVIII 


XIX 


FIG.  122.— Stellar  neighbors  of  the  sun. 

and  in  the  preceding  table  the  distances  of  the  stars  from 
the  sun  are  expressed  in  terms  of  this  unit.  To  express 
them  in  miles  the  numbers  in  the  table  must  be  multi- 
plied by  93,000,000,000,000.  The  nearest  star,  a  Centauri, 
is  25,000,000,000,000  miles  away.  But  there  is  another 
unit  in  more  common  use — i.  e.,  the  distance  traveled  over 


302  ASTRONOMY 

by  light  in  the  period  of  one  year.  We  have  already  found 
(§  141)  that  it  requires  light  8m.  18s.  to  come  from  the  sun 
to  the  earth,  and  it  is  a  simple  matter  to  find  from  this 
datum  that  in  a  year  light  moves  over  a  space  equal  to 
63,368  radii  of  the  earth's  orbit.  This  distance  is  called  a 
light  year,  and  the  distance  of  the  same  star,  a  Centauri, 
expressed  in  terms  of  this  unit,  is  4.26  years — i.  e.,  it  takes 
light  that  long  to  come  from  the  star  to  the  earth. 

In  Fig.  122  the  stellar  magnitudes  of  the  stars  are  indi- 
cated by  the  size  of  the  dots — the  bigger  the  dot  the  brighter 
the  star — and  a  mere  inspection  of  the  figure  will  serve  to 
show  that  within  a  radius  of  30  light  years  from  the  sun 
bright  stars  and  faint  ones  are  mixed  up  together,  and  that, 
so  far  as  distance  is  concerned,  the  sun  is  only  a  member 
of  this  swarm  of  stars,  whose  distances  apart,  each  from  its 
nearest  neighbor,  are  of  the  same  order  of  magnitude  as 
those  which  separate  the  sun  from  the  three  or  four  stars 
nearest  it. 

Fig.  122  is  not  to  be  supposed  complete.  Doubtless 
other  stars  will  be  found  whose  distance  from  the  sun  is  less 
than  2,000,000  radii  of  the  earth's  orbit,  but  it  is  not  prob- 
able that  they  will  ever  suffice  to  more  than  double  or  per- 
haps treble  the  number  here  shown.  The  vast  majority  of 
the  stars  lie  far  beyond  the  limits  of  the  figure. 

191.  Proper  motions. — It  is  evident  that  these  stars  are  too 
far  apart  for  their  mutual  attractions  to  have  much  influ- 
ence one  upon  another,  and  that  we  have  here  a  case  in  which, 
according  to  §  34,  each  star  is  free  to  keep  unchanged  its 
state  of  rest  or  motion  with  unvarying  velocity  along  a 
straight  line.  Their  very  name,  fixed  stars,  implies  that 
they  are  at  rest,  and  so  astronomers  long  believed.  Hippar- 
chus  (125  B.  c.)  and  Ptolemy  (130  A.  D.)  observed  and  re- 
corded many  allineations  among  the  stars,  in  order  to  give 
to  future  generations  a  means  of  settling  this  very  question 
of  a  possible  motion  of  the  stars  and  a  resulting  change  in 
their  relative  positions  upon  the  sky.  For  example,  they 


THE  FIXED  STARS  303 

found  at  the  beginning  of  the  Christian  era  that  the  four 
stars,  Capella,  e  Persei,  a  and  (3  Arietis,  stood  in  a  straight 
line — i.  e.,  upon  a  great  circle  of  the  sky.  Verify  this  by 
direct  reference  to  the  sky,  and  see  how  nearly  these  stars 
have  kept  the  same  position  for  nearly  twenty  centuries. 
Three  of  them  may  be  identified  from  the  star  maps,  and  the 
fourth,  e  Persei,  is  a  third-magnitude  star  between  Capella 
and  the  other  two. 

Other  allineations  given  by  Ptolemy  are :  Spica,  Arc- 
turus  and  ft  Bootis ;  Spica,  8  Corvi  and  y  Corvi ;  a  Librse, 
Arcturus  and  £  Ursas  Majoris.  Arcturus  does  not  now  fit 
very  well  to  these  alignments,  and  nearly  two  centuries 
ago  it,  together  with  Aldebaran  and  Sirius,  was  on  other 
grounds  suspected  to  have  changed  its  place  in  the  sky 
since  the  days  of  Ptolemy.  This  discovery,  long  since 
fully  confirmed,  gave  a  great  impetus  to  observing  with  all 
possible  accuracy  the  right  ascensions  and  declinations  of  the 
stars,  with  a  view  to  finding  other  cases  of  what  was  called 
proper  motion — i.  e.,  a  motion  peculiar  to  the  individual 
star  as  contrasted  with  the  change  of  right  ascension  and 
declination  produced  for  all  stars  by  the  precession. 

Since  the  middle  of  the  eighteenth  century  there  have 
been  made  many  thousands  of  observations  of  this  kind, 
whose  results  have  gone  into  star  charts  and  star  cata- 
logues, and  which  are  now  being  supplemented  by  a  photo- 
graphic survey  of  the  sky  that  is  intended  to  record  per- 
manently upon  photographic  plates  the  position  and  mag- 
nitude of  every  star  in  the  heavens  down  to  the  fourteenth 
magnitude,  with  a  view  to  ultimately  determining  all  their 
proper  motions. 

The  complete  achievement  of  this  result  is,  of  course,  a 
thing  of  the  remote  future,  but  sufficient  progress  in  deter- 
mining these  motions  has  been  made  during  the  past  cen- 
tury and  a  half  to  show  that  nearly  every  lucid  star  pos- 
sesses some  proper  motion,  although  in  most  cases  it  is  very 
small,  there  being  less  than  100  known  stars  in  which  it 


304  ASTRONOMY 

amounts  to  so  much  as  1"  per  annum — i.  e.,  a  rate  of  mo- 
tion across  the  sky  which  would  require  nearly  the  whole 
Christian  era  to  alter  a  star's  direction  from  us  by  so  much 
as  the  moon's  angular  diameter.  The  most  rapid  known 
proper  motion  is  that  of  a  telescopic  star  midway  between 
the  equator  and  the  south  pole,  which  changes  its  position 
at  the  rate  of  nearly  9"  per  annum,  and  the  next  greatest  is 
that  of  another  telescopic  star,  in  the  northern  sky,  No.  28 
of  Fig.  122.  It  is  not  until  we  reach  the  tenth  place  in  a 
list  of  large  proper  motions  that  we  find  a  bright  lucid 
star,  No.  1  of  Fig.  122.  It  is  a  significant  fact  that  for  the 
most  part  the  stars  with  large  proper  motions  are  precisely 
the  ones  shown  in  Fig.  122,  which  is  designed  to  show  stars 
near  the  earth.  This  connection  between  nearness  and 
rapidity  of  proper  motions  is  indeed  what  we  should  expect 
to  find,  since  a  given  amount  of  real  motion  of  the  star 
along  its  orbit  will  produce  a  larger  angular  displacement, 
proper  motion,  the  nearer  the  star  is  to  the  earth,  and  this 
fact  has  guided  astronomers  in  selecting  the  stars  to  be 
observed  for  parallax,  the  proper  motion  being  determined 
first  and  the  parallax  afterward. 

192.  The  paths  of  the  stars. — We  have  already  seen  rea- 
son for  thinking  that  the  orbit  along  which  a  star  moves  is 
practically  a  straight  line,  and  from  a  study  of  proper  mo- 
tions, particularly  their  directions  across  the  sky,  it  appears 
that  these  orbits  point  in  all  possible  ways— north,  south, 
east,  and  west — so  that  some  of  them  are  doubtless  directed 
nearly  toward  or  from  the  sun ;  others  are  square  to  the 
line  joining  sun  and  star;  while  the  vast  majority  occupy 
some  position  intermediate  between  these  two.  Now,  our 
relation  to  these  real  motions  of  the  stars  is  well  illus- 
trated in  Fig.  112,  where  the  observer  finds  in  some  of  the 
shooting  stars  a  tremendous  proper  motion  across  the  sky, 
but  sees  nothing  of  their  rapid  approach  to  him,  while 
others  appear  to  stand  motionless,  although,  in  fact,  they 
are  moving  quite  as  rapidly  as  are  their  fellows.  The  fixed 


THE  FIXED  STARS  305 

star  resembles  the  shooting  star  in  this  respect,  that  its 
proper  motion  is  only  that  part  of  its  real  motion  which 
lies  at  right  angles  to  the  line  of  sight,  and  this  needs  to 
he  supplemented  by  that  other  part  of  the  motion  which 
lies  parallel  to  the  line  of  sight,  in  order  to  give  us  any 
knowledge  of  the  star's  real  orbit. 

193.  Motion  in  the  line  of  sight. — It  is  only  within  the 
last  25  years  that  anything  whatever  has  been  accomplished 
in  determining  these  stellar  motions  of  approach  or  reces- 
sion, but  within  that  time  much  progress  has  been  made  by 
applying  the  Doppler  principle  (§  89)  to  the  study  of  stel- 
lar spectra,  and  at  the  present  time  nearly  every  great  tele- 
scope in  the  world  is  engaged  upon  work  of  this  kind.  The 
shifting  of  the  lines  of  the  spectrum  toward  the  violet  or 


4450  4500  4550 


FIG.  123.— Motion  of  Polaris  in  the  line  of  sight  as  determined  by  the  spectroscope. 

FBOST. 

toward  the  red  end  of  the  spectrum  indicates  with  cer- 
tainty the  approach  or  recession  of  the  star,  but  this  shift- 
ing, which  must  be  determined  by  comparing  the  star's 
spectrum  with  that  of  some  artificial  light  showing  corre- 
sponding lines,  is  so  small  in  amount  that  its  accurate  meas- 
urement is  a  matter  or  extreme  difficulty,  as  may  be  seen 
from  Fig.  123.  This  cut  shows  along  its  central  line  a  part 
of  the  spectrum  of  Polaris,  between  wave  lengths  4,450  and 
4,600  tenth  meters,  while  above  and  below  are  the  corre- 
sponding parts  of  the  spectrum  of  an  electric  spark  whose 
light  passed  through  the  same  spectroscope  and  was  photo- 
graphed upon  the  same  plate  with  that  of  Polaris.  This 
comparison  spectrum  is,  as  it  should  be,  a  discontinuous  or 
bright-line  one,  while  the  spectrum  of  the  star  is  a  con- 


306  ASTRONOMY 

tinuous  one,  broken  only  by  dark  gaps  or  lines,  many  of 
which  have  no  corresponding  lines  in  the  comparison  spec- 
trum. But  a  certain  number  of  lines  in  the  two  spectra 
do  correspond,  save  that  the  dark  line  is  always  pushed  a 
very  little  toward  the  direction  of  shorter  wave  lengths, 


111    I    I 

FIG.  124.— Spectrum  of  /3  Aurigae.— PICKERING. 

showing  that  this  star  is  approaching  the  earth.  This  spec- 
trum was  photographed  for  the  express  purpose  of  deter- 
mining the  star's  motion  in  the  line  of  sight,  and  with  it 
there  should  be  compared  Figs.  124  and  125,  which  show 
in  the  upper  part  of  each  a  photograph  obtained  without 
comparison  spectra  by  allowing  the  star's  light  to  pass 
through  some  prisms  placed  just  in  front  of  the  telescope. 
The  lower  section  of  each  figure  shows  an  enlargement  of 
the  original  photograph,  bringing  out  its  details  in  a  way 
not  visible  to  the  unaided  eye.  In  the  enlarged  spectrum 
of  /?  Aurigas  a  rate  of  motion  equal  to  that  of  the  earth  in 
its  orbit  would  be  represented  by  a  shifting  of  0.03  of  a 
millimeter  in  the  position  of  the  broad,  hazy  lines. 

Despite  the  difficulty  of  dealing  with  such  small  quanti- 
ties as  the  above,  very  satisfactory  results  are  now  obtained, 
and  from  them  it  is  known  that  the  velocities  of  stars  in 
the  line  of  sight  are  of  the  same  order  of  magnitude  as  the 
velocities  of  the  planets  in  their  orbits,  ranging  all  the  way 
from  0  to  60  miles  per  second — more  than  200,000  miles  per 
hour — which  latter  velocity,  according  to  Campbell,  is  the 
rate  at  which  ^  Cassiopeise  is  approaching  the  sun. 


THE   FIXED  STARS  307 

The  student  should  not  fail  to  note  one  important 
difference  between  proper  motions  and  the  motions  deter- 
mined spectroscopically  :  the  latter  are  given  directly  in 
miles  per  second,  or  per  hour,  while  the  former  are  ex- 
pressed in  angular  measure,  seconds  of  arc,  and  there  can 
be  no  direct  comparison  between  the  two  until  by  means 
of  the  known  distances  of  the  stars  their  proper  motions 
are  converted  from  angular  into  linear  measure.  We  are 
brought  thus  to  the  very  heart  of  the  matter ;  parallax, 
proper  motion,  and  motion  in  the  line  of  sight  are  inti- 


;  t  lii  1  i  i.HitllHil!  Ill  I  11  i       II    ' 

HI  III  I        i  i 


:. 

FIG.  125.— Spectrum  of  Pollux.— PICKERING. 

mately  related  quantities,  all  of  which  are  essential  to  a 
knowledge  of  the  real  motions  of  the  stars. 

194.  Star  drift. — An  illustration  of  how  they  may  be 
made  to  work  together  is  furnished  by  some  of  the  stars 
—which  make  up  the  Great  Dipper — /3,  y,  €,  and  £  Ursae  Ma- 
joris,  whose  proper  motions  have  long  been  known  to  point 
in  nearly  the  same  direction  across  the  sky  and  to  be  nearly 
equal  in  amount.  More  recently  it  has  been  found  that 
these  stars  are  all  moving  toward  the  sun  with  approxi- 
mately the  same  velocity — 18  miles  per  second.  One  other 
star  of  the  Dipper,  8  Ursae  Majoris,  shares  in  the  common 
proper  motion,  but  its  velocity  in  the  line  of  sight  has  not 
yet  been  determined  with  the  spectroscope.  These  similar 
motions  make  it  probable  that  the  stars  are  really  traveling 
together  through  space  along  parallel  lines;  and  on  the 


308 


ASTRONOMY 


supposition  that  such  is  the  case  it  is  quite  possible  to 
write  out  a  set  of  equations  which  shall  involve  their 
known  proper  motions  and  motions  in  the  line  of  sight, 
together  with  their  unknown  distances  and  the  unknown 
direction  and  velocity  of  their  real  motion  along  their 
orbits.  Solving  these  equations  for  the  values  of  the  un- 
known quantities,  it  is  found  that  the  five  stars  probably 
lie  in  a  plane  which  is  turned  nearly  edgewise  toward  us, 
and  that  in  this  plane  they  are  moving  about  twice  as  fast 
as  the  earth  moves  around  the  sun,  and  are  at  a  distance 
from  us  represented  by  a  parallax  of  less  than  0.02" — i.  e., 
six  times  as  great  as  the  outermost  circle  in  Fig.  122.  A 
most  extraordinary  system  of  stars  which,  although  sepa- 
rated from  each  oth- 
er by  distances  as 
great  as  the  whole 
breadth  of  Fig.  122, 
yet  move  along  in 
parallel  paths  which 
it  is  difficult  to  re- 
gard as  the  result 
of  chance,  and  for 
which  it  is  equally 
difficult  to  frame  an 
explanation. 

The  stars  a  and 
rj  of  the  Great  Dip- 
per do  not  share 
in  this  motion,  and 
must  ultimately  part 
company  with  the 
other  five,  to  the 
complete  destruction 

of  the  Dipper's  shape.  Fig.  126  illustrates  this  change  of 
shape,  the  upper  part  of  the  figure  (a)  showing  these  seven 
stars  as  they  were  grouped  at  a  remote  epoch  in  the  past, 


FIG.  126.— The  Great  Dipper,   past,  present,  and 
future. 


THE  FIXED   STARS  309 

while  the  lower  section  (c)  shows  their  position  for  an 
equally  remote  epoch  in  the  future.  There  is  no  resem- 
blance to  a  dipper  in  either  of  these  configurations,  but  it 
should  be  observed  that  in  each  of  them  the  stars  a  and  17 
keep  their  relative  position  unaltered,  and  the  other  five 
stars  also  keep  /together,  the  entire  change  of  appearance 
being  due  to/the  changing  positions  of  these  two  groups 
with  respect  to  each  other. 

This  phenomenon  of  groups  of  stars  moving  together  is 
called  star  drift,  and  quite  a  number  of  cases  of  it  are 
found  in  different  parts  of  the  sky.  The  Pleiades  are  per- 
haps the  most  conspicuous  one,  for  here  some  sixty  or 
more  stars  are  found  traveling  together  along  similar  paths. 
Eepeated  careful  measurements  of  the  relative  positions  of 
stars  in  this  cluster  show  that  one  of  the  lucid  stars  and 
four  or  five  of  the  telescopic  ones  do  not  share  in  this 
motion,  and  therefore  are  not  to  be  considered  as  members 
of  the  group,  but  rather  as  isolated  stars  which,  for  a  time, 
chance  to  be  nearly  on  line  with  the  Pleiades,  and  prob- 
ably farther  off,  since  their  proper  motions  are  smaller. 

To  rightly  appreciate  the  extreme  slowness  with  which 
proper  motions  alter  the  constellations,  the  student  should 
bear  in  mind  that  the  changes  shown  in  passing  from  one 
section  of  Fig.  126  to  the  next  represent  the  effect  of  the 
present  proper  motions  of  the  stars  accumulated  for  a  pe- 
riod of  200,000  years.  Will  the  stars  continue  to  move  in 
straight  paths  for  so  long  a  time  ? 

195.  The  sun's  way. — Another  and  even  more  interest- 
ing application  of  proper  motions  and  motions  in  the  line 
of  sight  is  the  determination  from  them  of  the  sun's  orbit 
among  the  stars.  The  principle  involved  is  simple  enough. 
If  the  sun  moves  with  respect  to  the  stars  and  carries  the 
earth  and  the  other  planets  year  after  year  into  new  regions 
of  space,  our  changing  point  of  view  must  displace  in  some 
measure  every  star  in  the  sky  save  those  which  happen  to 
be  exactly  on  the  line  of  the  sun's  motion,  and  even  these 


310  ASTRONOMY 

will  show  its  effect  by  their  apparent  motion  of  approach 
or  recession  along  the  line  of  sight.  So  far  as  their  own 
orbital  motions  are  concerned,  there  is  no  reason  to  sup- 
pose that  more  stars  move  north  than  south,  or  that  more 
go  east  than  west ;  and  when  we  find  in  their  proper  mo- 
tions a  distinct  tendency  to  radiate  from  a  point  some- 
where near  the  bright  star  Vega  and  to  converge  toward 
a  point  on  the  opposite  side  of  the  sky,  we  infer  that  this 
does  not  come  from  any  general  drift  of  the  stars  in  that 
direction,  but  that  it  marks  the  course  of  the  sun  among 
them.  That  it  is  moving  along  a  straight  line  pointing 
toward  Vega,  and  that  at  least  a  part  of  the  velocities 
which  the  spectroscope  shows  in  the  line  of  sight,  comes 
from  the  motion  of  the  sun  and  earth.  Working  along 
these  lines,  Kapteyn  finds  that  the  sun  is  moving  through 
space  with  a  velocity  of  11  miles  per  second,  which  is  de- 
cidedly below  the  average  rate  of  stellar  motion — 19  miles 
per  second. 

196.  Distance  of  Sirian  and  solar  stars, — By  combining 
this  rate  of  motion  of  the  sun  with  the  average  proper  mo- 
tions of  the  stars  of  different  magnitudes,  it  is  possible  to 
obtain  some  idea  of  the  average  distance  from  us  of  a  first- 
magnitude  star  or  a  sixth-magnitude  star,  which,  while  it 
gives  no  information  about  the  actual  distance  of  any  par- 
ticular star,  does  show  that  on  the  whole  the  fainter  stars 
are  more  remote.  But  here  a  broad  distinction  must  be 
drawn.  By  far  the  larger  part  of  the  stars  belong  to  one  of 
two  well-marked  classes,  called  respectively  Sirian  and  solar 
stars,  which  are  readily  distinguished  from  each  other  by 
the  kind  of -spectrum  they  furnish.  Thus  ft  Aurigse  belongs 
to  the  Sirian  class,  as  does  every  other  star  which  has  a  spec- 
trum like  that  of  Fig.  124,  while  Pollux  is  a  solar  star  pre- 
senting in  Fig.  125  a  spectrum  like  that  of  the  sun,  as  do 
the  other  stars  of  this  class. 

Two  thirds  of  the  sun's  near  neighbors,  shown  in  Fig. 
122,  have  spectra  of  the  solar  type,  and  in  general  stars  of 


THE  FIXED  STARS  311 

this  class  are  nearer  to  us  than  are  the  stars  with  spectra 
unlike  that  of  the  sun.  The  average  distance  of  a  solar 
star  of  the  first  magnitude  is  very  approximately  repre- 
sented hy  the  outer  circle  in  Fig.  122,  2,000,000  times  the 
distance  of  the  sun  from  the  earth ;  while  the  correspond- 
ing distance  for  a  Sirian  star  of  the  first  magnitude  is  rep- 
resented by  the  number  4,600,000. 

A  third-magnitude  star  is  on  the  average  twice  as  far 
away  as  one  of  the  first  magnitude,  a  fifth-magnitude  star 
four  times  as  far  off,  etc.,  each  additional  two  magnitudes 
doubling  the  average  distance  of  the  stars,  at  least  down  to 
the  eighth  magnitude  and  possibly  farther,  although  be- 
yond this  limit  we  have  no  certain  knowledge.  Put  in 
another  way,  the  naked  eye  sees  many  Sirian  stars  which 
may  have  "  gone  out "  and  ceased  to  shine  centuries  ago, 
for  the  light  by  which  we  now  see  them  left  those  stars 
before  the  discovery  of  America  by  Columbus.  For  the 
student  of  mathematical  tastes  we  note  that  the  results  of 
Kapteyn's  investigation  of  the  mean  distances  (D)  of  the 
stars  of  magnitude  (m)  may  be  put  into  two  equations  : 

m 

For  Solar  Stars,   D  =  23  X  2¥ 

m 

For  Sirian  Stars,  D  =  52  X  2* 

where  the  coefficients  23  and  52  are  expressed  in  light 
years.  How  long  a  time  is  required  for  light  to  come  from 
an  average  solar  star  of  the  sixth  magnitude  ? 

197.  Consequences  of  stellar  distance. — The  amount  of 
light  which  comes  to  us  from  any  luminous  body  varies 
inversely  as  the  square  of  its  distance,  and  since  many  of 
the  stars  are  changing  their  distance  from  us  quite  rapidly, 
it  must  be  that  with  the  lapse  of  time  they  will  grow 
brighter  or  fainter  by  reason  of  this  altered  distance. 
But  the  distances  themselves  are  so  great  that  the  most 
rapid  known  motion  in  the  line  of  sight  would  require 
more  than  1,000  years  (probably  several  thousand)  to  pro- 
duce any  perceptible  change  in  brilliancy. 


312  ASTRONOMY 

The  law  in  accordance  with  which  this  change  of  bril- 
liancy takes  place  is  that  the  distance  must  be  increased  or 
diminished  tenfold  in  order  to  produce  a  change  of  five 
magnitudes  in  the  brightness  of  the  object,  and  we  may 
apply  this  law  to  determine  the  sun's  rank  among  the  stars. 
If  it  were  removed  to  the  distance  of  an  average  first-,  or 
second-,  or  third-magnitude  star,  how  would  its  light  com- 
pare with  that  of  the  stars  ?  The  average  distance  of  a 
third-magnitude  star  of  the  solar  type  is,  as  we  have  seen 
above,  4,000,000  times  the  sun's  distance  from  the  earth, 
and  since  4,000,000  =  106-6,  we  find  that  at  this  distance  the 
sun's  stellar  magnitude  would  be  altered  by  6.6  X  5  magni- 
tudes, and  would  therefore  be  —26.5  +  33.0  =  6.5 — i.  e.,  the 
sun  if  removed  to  the  average  distance  of  the  third-magni- 
tude stars  of  its  type  would  be  reduced  to  the  very  limit 
of  naked-eye  visibility.  It  must  therefore  be  relatively 
small  and  feeble  as  compared  with  the  brightness  of  the 
average  star.  It  is  only  its  close  proximity  to  us  which 
makes  the  sun  look  brighter  than  the  stars. 

The  fixed  stars  may  have  planets  circling  around  them, 
but  an  application  of  the  same  principles  will  show  how 
hopeless  is  the  prospect  of  ever  seeing  them  in  a  telescope. 
If  the  sun's  nearest  neighbor,  a  Centauri,  were  attended  by 
a  planet  like  Jupiter,  this  planet  would  furnish  to  us  no 
more  light  than  does  a  star  of  the  twenty-second  magni- 
tude— i.  e.,  it  would  be  absolutely  invisible,  and  would  re- 
main invisible  in  the  most  powerful  telescope  yet  built, 
even  though  its  bulk  were  increased  to  equal  that  of  the 
sun.  Let  the  student  make  the  computation  leading  to 
this  result,  assuming  the  stellar  magnitude  of  Jupiter  to 
be  -1.7. 

198.  Double  stars, — In  the  constellation  Taurus,  not  far 
from  Aldebaran,  is  the  fourth-magnitude  star  6  Tauri, 
which  can  readily  be  seen  to  consist  of  two  stars  close 
together.  The  star  a  Capricorni  is  plainly  double,  and  a 
sharp  eye  can  detect  that  one  of  the  faint  stars  which  with 


THE  FIXED  STARS  313 

Vega  make  a  small  equilateral  triangle,  is  also  a  double 
star.  Look  for  them  in  the  sky. 

In  the  strict  language  of  astronomy  the  term  double 
star  would  not  be  applied  to  the  first  two  of  these  objects, 
since  it  is  usually  restricted  to  those  stars  whose  angular 
distance  from  each  other  is  so  small  that  in  the  telescope 
they  appear  much  as  do  the  stars  named  above  to  the  naked 
eye — i.  e.,  their  angular  separation  is  measured  by  a  few 
seconds  or  fractions  of  a  single  second,  instead  of  the  six 
minutes  which  separate  the  component  stars  of  0  Tauri  or 
a  Capricorni.  There  are  found  in  the  sky  many  thousands 
of  these  close  double  stars,  of  which  some  are  only  optic- 
ally double — i.  e.,  two  stars  nearly  on  line  with  the  earth 
but  at  very  different  distances  from  it— while  more  of  them 
are  really  what  they  seem,  stars  near  each  other,  and  in 
many  cases  near  enough  to  influence  each  other's  motion. 
These  are  called  binary  systems,  and  in  cases  of  this  kind 
the  principles  of  celestial  mechanics  set  forth  in  Chapter 
IV  hold  true,  and  we  may  expect  to  find  each  component 
of  a  double  star  moving  in  a  conic  section  of  some  kind, 
having  its  focus  at  the  common  center  of  gravity  of  the 
two  stars.  We  are  thus  presented  with  problems  of  orbital 
motion  quite  similar  to  those  which  occur  in  the  solar  sys- 
tem, and  careful  telescopic  observations  are  required  year 
after  year  to  fix  the  relative  positions  of  the  two  stars — i.  e., 
their  angular  separation,  which  it  is  customary  to  call  their 
distance,  and  their  direction  one  from  the  other,  which  is 
called  position  angle. 

199.  Orbits  of  double  stars. — The  sun's  nearest  neighbor, 
a  Centauri,  is  such  a  double  star,  whose  position  angle  and 
distance  have  been  measured  by  successive  generations  of 
astronomers  for  more  than  a  century,  and  Fig.  127  shows 
the  result  of  plotting  their  observations.  Each  black  dot 
that  lies  on  or  near  the  circumference  of  the  long  ellipse 
stands  for  an  observed  direction  and  distance  of  the  fainter 
of  the  two  stars  from  the  brighter  one,  which  is  represented 
21 


314 


ASTRONOMY 


by  the  small  circle  at  the  intersection  of  the  lines  inside 
the  ellipse.  It  appears  from  the  figure  that  during  this 

time  the  one  star  has 
gone  completely  around 
the  other,  as  a  planet 
goes  around  the  sun, 
and  the  true  orbit  must 
therefore  be  an  ellipse 
having  one  of  its  foci 
at  the  center  of  gravity 
of  the  two  stars.  The 
other  star  moves  in  an 
ellipse  of  precisely  simi- 
lar shape,  but  probably 
smaller  size,  since  the 
dimensions  of  the  two 
FIG.  is?.— The  orbit  of  a  Centauri.— SEE.  orbits  are  inversely  pro- 

portional  to  the  masses 

of  the  two  bodies,  but  it  is  customary  to  neglect  this  motion 
of  the  larger  star  and  to  give  to  the  smaller  one  an  orbit 
whose  diameter  is  equal  to  the  sum  of  the  diameters  of  the 
two  real  orbits.  This  practice,  which  has  been  followed  in 
Fig.  127,  gives  correctly  the  relative  positions  of  the  two 
stars,  and  makes  one  orbit  do  the  work  of  two. 

In  Fig.  127  the  bright  star  does  not  fall  anywhere  near 
the  focus  of  the  ellipse  marked  out  by  the  smaller  one,  and 
from  this  we  infer  that  the  figure  does  not  show  the  true 
shape  of  the  orbit,  which  is  certainly  distorted,  foreshort- 
ened, by  the  fact  that  we  look  obliquely  down  upon  its 
plane.  It  is  possible,  however,  by  mathematical  analysis, 
to  find  just  how  much  and  in  what  direction  that  plane 
should  be  turned  in  order  to  bring  the  focus  of  the 
ellipse  up  to  the  position  of  the  principal  star,  and  thus 
give  the  true  shape  and  size  of  the  orbit.  See  Fig.  128 
for  a  case  in  which  the  true  orbit  is  turned  exactly  edge- 
wise toward  the  earth,  and  the  small  star,  which  really 


THE  FIXED  STABS 


315 


moves  in  an  ellipse  like  that  shown  in  the  figure,  appears 
to  oscillate  to  and  fro  along  a  straight  line  drawn  through 
the  principal  star,  as  shown  at  the  left  of  the  figure. 

In  the  case  of  a 
Centauri  the  true  orbit 
proves  to  have  a  major 
axis  47  times,  and  a 
minor  axis  40  times, 
as  great  as  the  distance 
of  the  earth  from  the 
sun.  The  orbit,  in 
fact,  is  intermediate 
in  size  between  the 
orbits  of  Uranus  and 
Xeptune,  and  the  pe- 
riodic time  of  the  star 
in  this  orbit  is  81 
years,  a  little  less  than 
the  period  of  Uranus. 

200.  Masses  of  double  stars.  —  If  we  apply  to  this  orbit 
Kepler's  Third  Law  in  the  form  given  it  at  page  179,  we 
shall  find— 


FIG.  128. — Apparent  orbit  and  real  orbit  of  the 
double  star  42  Comse  Berenicis. — SEE. 


where  M  and  m  represent  the  masses  of  the  two  stars.  We 
have  already  seen  that  &,  the  gravitation  constant,  is  equal 
to  1  when  the  masses  are  measured  in  terms  of  the  sun's 
mass  taken  as  unity,  and  when  T  and  a  are  expressed  in 
years  and  radii  of  the  earth's  orbit  respectively,  and  with 
this  value  of  Ic  we  may  readily  find  from  the  above  equa- 
tion, M-\-m  =  2.5  —  i.  e.,  the  combined  mass  of  the  two  com- 
ponents of  a  Centauri  is  equal  to  rather  more  than  twice 
the  mass  of  the  sun.  It  is  not  every  double  star  to  which 
this  process  of  weighing  can  be  applied.  The  major  axis 
of  the  orbit,  #,  is  found  from  the  observations  in  angular 
measure,  35"  in  this  case,  and  it  is  only  when  the  parallax 


316 


ASTRONOMY 


of  the  star  is  known  that  this  can  be  converted  into  the 
required  linear  units,  radii  of  the  earth's  orbit,  by  dividing 
the  angular  major  axis  by  the  parallax ;  47  =  35"  -j-  0.75". 
Our  list  of  distances  (§  189)  contains  six  double  stars 
whose  periodic  times  and  major  axes  have  been  fairly  well 
determined,  and  we  find  in  the  accompanying  table  the  in- 
formation which  they  give  about  the  masses  of  double  stars 
and  the  size  of  the  orbits  in  which  they  move  : 


STAR. 

Major  axis. 

Minor  axis. 

Periodic 
time. 

Mass. 

t\  CassiopGisB 

66 

56 

196 

1 

o'2  Eridani     .       ... 

i         63 

62 

139 

2 

a  Centauri  

47 

40 

81 

2 

70  Ophiuchi  

....         56 

48 

88 

3 

Procyon 

...         34 

31 

40 

3 

Sirius              .       .    . 

I         43 

34 

52 

4 

The  orbit  of  Uranus,  diameter  =  38,  and  Neptune,  diam- 
eter =  60,  are  of  much  the  same  size  as  these  double-star 
orbits ;  but  the  planetary  orbits  are  nearly  circular,  while 
in  every  case  the  double  stars  show  a  substantial  difference 
between  the  long  and  short  diameters  of  their  orbits.  This 
is  a  characteristic  feature  of  most  double-star  orbits,  and 
seems  to  stand  in  some  relation  to  their  periodic  times,  for, 
on  the  average,  the  longer  the  time  required  by  a  star  to 
make  its  orbital  revolution  the  more  eccentric  is  its  orbit 
likely  to  prove. 

Another  element  of  the  orbits  of  double  stars,  which 
stands  in  even  closer  relation  to  the  periodic  time,  is  the 
major  axis ;  the  smaller  the  long  diameter  of  the  orbit  the 
more  rapid  is  the  motion  and  the  shorter  the  periodic  time, 
so  that  astronomers  in  search  of  interesting  double-star 
orbits  devote  themselves  by  preference  to  those  stars  whose 
distance  apart  is  so  small  that  they  can  barely  be  distin- 
guished one  from  the  other  in  the  telescope. 

Although  the  half-dozen  stars  contained  in  the  table 
all  have  orbits  of  much  the  same  size  and  with  much  the 


THE  FIXED  STARS  31Y 

same  periodic  time  as  those  in  which  Uranus  and  Neptune 
move,  this  is  by  no  means  true  of  all  the  double  stars,  many 
of  which  have  periods  running  up  into  the  hundreds  if  not 
thousands  of  years,  while  a  few  complete  their  orbital  revo- 
lutions in  periods  comparable  with,  or  even  shorter  than, 
that  of  Jupiter. 

201.  Dark  stars. — Procyon,  the  next  to  the  last  star  of 
the  preceding  table,  calls  for  some  special  mention,  as  the 
determination  of  its  mass  and  orbit  stands  upon  a  rather 
different  basis  from  that  of  the  other  stars.  More  than 
half  a  century  ago  it  was  discovered  that  its  proper  motion 
was  not  straight  and  uniform  after  the  fashion  of  ordinary 
stars,  but  presented  a  series  of  loops  like  those  marked  out 
by  a  bright  point  on  the  rim  of  a  swiftly  running  bicycle 
wheel.  The  hub  may  move  straight  forward  with  uniform 
velocity,  but  the  point  near  the  tire  goes  up  and  down,  and, 
while  sharing  in  the  forward  motion  of  the  hub,  runs  some- 
times ahead  of  it,  sometimes  behind,  and  such  seemed  to 
be  the  motion  of  Procyon  and  of  Sirius  as  well.  Bessel, 
who  discovered  it,  did  not  hesitate  to  apply  the  laws  of  mo- 
tion, and  to  affirm  that  this  visible  change  of  the  star's 
motion  pointed  to  the  presence  of  an  unseen  companion, 
which  produced  upon  the  motions  of  Sirius  and  Procyon 
just  such  effects  as  the  visible  companions  produce  in  the 
motions  of  double  stars.  A  new  kind  of  star,  dark  instead 
of  bright,  was  added  to  the  astronomer's  domain,  and  its 
discoverer  boldly  suggested  the  possible  existence  of  many 
more.  "  That  countless  stars  are  visible  is  clearly  no  argu- 
ment againsu  the  existence  of  as  many  more  invisible  ones." 
"  There  is  no  reason  to  think  radiance  a  necessary  property 
of  celestial  bodies."  But  most  astronomers  were  incredu- 
lous, and  it  was  not  until  1862  that,  in  the  testing  of  a  new 
and  powerful  telescope  just  built,  a  dark  star  was  brought 
to  light  and  the  companion  of  Sirius  actually  seen.  The 
visual  discovery  of  the  dark  companion  of  Procyon  is 
of  still  more  recent  date  (November,  1896),  when  it  was 


318  ASTRONOMY 

detected  with  the  great  telescope  of  the  Lick  Observatory. 
This  discovery  is  so  recent  that  the  orbit  is  still  very  uncer- 
tain, being  based  almost  wholly  upon  the  variations  in  the 
proper  motion  of  the  star,  and  while  the  periodic  time  must 
be  very  nearly  correct,  the  mass  of  the  stars  and  dimensions 
of  the  orbit  may  require  considerable  correction. 

The  companion  of  Sirius  is  about  ten  magnitudes  and 
that  of  Procyon  about  twelve  magnitudes  fainter  than  the 
star  itself.  How  much  more  light  does  the  bright  star  give 
than  its  faint  companion  ?  Despite  the  tremendous  differ- 
ence of  brightness  represented  by  the  answer  to  this  ques- 
tion, the  mass  of  Sirius  is  only  about  twice  as  great  as 
that  of  its  companion,  and  for  Procyon  the  ratio  does  not 
exceed  five  or  six.  / 

The  visual  discovery  of  the  companions  to  Sirius  and 
Procyon  removes  them  from  the  list  of  dark  stars,  but 
others  still  remain  unseen,  although  their/existence  is  in- 
dicated by  variable  proper  motions  oi^Jtfy  variable  orbital 
motion,  as  in  the  case  of  £  Cancri,  where  one  of  the  compo- 
nents of  a  triple  star  moves  around  the  other  two  in  a  series 
of  loops  whose  presence  indicates  a  disturbing  body  which 
has  never  yet  been  seen. 

202.  Multiple   stars. — Combinations   of  three,  four,   or 
more  stars  close  to  each  other,  like  £  Cancri,  are  called  mul- 
tiple stars,  and  while  they  are  far  from  being  as  common  as 
are  double  stars,  there  is  a  considerable  number  of  them  in 
the  sky,  100  or  more  as  against  the  more  than  10,000  dou- 
ble stars  that  are  known.     That  their  relative  motions  are 
subject  to  the  law  of  gravitation  admits  of  no  serious  doubt, 
but  mathematical  analysis  breaks  down  in  face  of  the  diffi- 
culties here  presented,  and  no  astronomer  has  ever  been 
able  to  determine  what  will  be  the  general  character  of 
the  motions  in  such  a  system. 

203.  Spectroscopic  binaries. — In  the  year  1890  Professor 
Pickering,  of  the  Harvard  Observatory,  announced  the  dis- 
covery of  a  new  class  of  double  stars,  invisible  as  such  in 


THE  FIXED  STARS  319 

even  the  most  powerful  telescope,  and  producing  no  per- 
turbations such  as  have  been  considered  above,  but  show- 
ing in  their  spectrum  that  two  or  more  bodies  must  be 
present  in  the  source  of  light  which  to  the  eye  is  indistin- 
guishable from  a  single  star.  In  Fig.  129  we  suppose  A 
and  B  to  be  the  two  components  of  a  double  star,  each 
moving  in  its  own  orbit  about  their  common  center  of 


To  the  Earth 


A 
FIG.  129.— Illustrating  the  motion  of  a  spectroscopic  binary. 

gravity,  C\  whose  distance  from  the  earth  is  several  million 
times  greater  than  the  distance  between  the  stars  them- 
selves. Under  such  circumstances  no  telescope  could  dis- 
tinguish between  the  two  stars,  which  would  appear  fused 
into  one ;  but  the  smaller  the  orbit  the  more  rapid  would 
be  their  motion  in  it,  and  if  this  orbit  were  turned  edgewise 
toward  the  earth,  as  is  supposed  in  the  figure,  whenever 
the  stars  were  in  the  relative  position  there  shown,  A  would 
be  rapidly  approaching  the  earth  by  reason  of  its  orbital 
motion,  while  B  would  move  away  from  it,  so  that  in 
accordance  with  the  Doppler  principle  the  lines  composing 
their  respective  spectra  would  be  shifted  in  opposite  direc- 
tions, thus  producing  a  doubling  of  the  lines,  each  single 
line  breaking  up  into  two,  like  the  double-sodium  line  Z>, 
only  not  spaced  so  far  apart.  When  the  stars  have  moved 
a  quarter  way  round  their  orbit  to  the  points  A1,  B',  their 
velocities  are  turned  at  right  angles  to  the  line  of  sight 


320  ASTRONOMY 

and  the  spectrum  returns  to  the  normal  type  with  single 
lines,  only  to  break  up  again  when  after  another  quarter 
revolution  their  velocities  are  again  parallel  with  the  line 
of  sight.  The  interval  of  time  between  consecutive  dou- 
blings of  the  lines  in  the  spectrum  thus  furnishes  half 
the  time  of  a  revolution  in  the  orbit.  The  distance  be- 
tween the  components  of  a  double  line  shows  by  means  of 
the  Doppler  principle  how  fast  the  stars  are  traveling,  and 
this  in  connection  with  the  periodic  times  fixes  the  size 
of  the  orbit,  provided  we  assume  that  it  is  turned  exactly 
edgewise  to  the  earth.  This  assumption  may  not  be  quite 
true,  but  even  though  the  orbit  should  deviate  consider- 
ably from  this  position,  it  will  still  present  the  phenomenon 
of  the  double  lines  whose  displacement  will  now  show  some- 
thing less  than  the  true  velocities  of  the  stars  in  their  or- 
bits, since  the  spectroscope  measures  only  that  component 
of  the  whole  velocity  which  is  directed  toward  the  earth, 
and  it  is  important  to  note  that  the  real  orbits  and  masses 
of  these  spectroscopic  binaries,  as  they  are  called,  will  usu- 
ally be  somewhat  larger  than  those  indicated  by  the  spec- 
troscope, since  it  is  only  in  exceptional  cases  that  the  orbit 
will  be  turned  exactly  edgewise  to  us. 

The  bright  star  Capella  is  an  excellent  illustration  of 
these  spectroscopic  binaries.  At  intervals  of  a  little  less 
than  a  month  the  lines  of  its  spectrum  are  alternately 
single  and  double,  their  maximum  separation  correspond- 
ing to  a  velocity  in  the  line  of  sight  amounting  to  37  miles 
per  second.  Each  component  of  a  doubled  line  appears  to 
be  shifted  an  equal  amount  from  the  position  occupied  by 
the  line  when  it  is  single,  thus  indicating  equal  velocities 
and  equal  masses  for  the  two  component  stars  whose  peri- 
odic time  in  their  orbit  is  104  days.  From  this  periodic 
time,  together  with  the  velocity  of  the  star's  motion,  let  the 
student  show  that  the  diameter  of  the  orbit — i.  e.,  the  dis- 
tance of  the  stars  from  each  other — is  approximately  53,000,- 
000  miles,  and  that  their  combined  mass  is  a  little  less  than 


THE  FIXED  STARS  321 

that  of  a  Centauri,  provided  that  their  orbit  plane  is  turned 
exactly  edgewise  toward  the  earth. 

There  are  at  the  present  time  (1901)  34  spectroscopic 
binaries  known,  including  among  them  such  stars  as  Pola- 
ris, Capella,  Algol,  Spica,  (3  Aurigae,  £  Ursae  Majoris,  etc., 
and  their  number  is  rapidly  increasing,  about  one  star  out  of 
every  nine  whose  motion  in  the  line  of  sight  is  determined 
proving  to  be  a  binary  or,  as  in  the  case  of  Polaris,  possibly 
triple.  On  account  of  smaller  distance  apart  their  periodic 
times  are  much  shorter  than  those  of  the  ordinary  double 
stars,  and  range  from  a  few  days  up  to  several  months — 
more  than  two  years  in  the  case  of  y  Pegasi,  which  has  the 
longest  known  period  of  any  star  of  this  class. 

Spectroscopic  binaries  agree  with  ordinary  double  stars 
in  having  masses  rather  greater  than  that  of  the  sun,  but 
there  is  as  yet  no  assured  case  of  a  mass  ten  times  as  great 
as  that  of  the  sun. 

204.  Variable  stars. — Attention  has  already  been  drawn 
(§23)  to  the  fact  that  some  stars  shine  with  a  changing 
brightness — e.  g.,  Algol,  the  most  famous  of  these  variable 
stars,  at  its  maximum  of  brightness  furnishes  three  times 
as  much  light  as  when  at  its  minimum,  and  other  variable 
stars  show  an  even  greater  range.  The  star  o  Ceti  has  been 
named  Mira  (Latin,  the  wonderful),  from  its  extraordinary 
range  of  brightness,  more  than  six-hundred-fold.  For  the 
greater  part  of  the  time  this  star  is  invisible  to  the  naked 
eye,  but  during  some  three  months  in  every  year  it  bright- 
ens up  sufficiently  to  be  seen,  rising  quite  rapidly  to  its 
maximum  brilliancy,  which  is  sometimes  that  of  a  second- 
magnitude  star,  but  more  frequently  only  third  or  even 
fourth  magnitude,  and,  after  shining  for  a  few  weeks  with 
nearly  maximum  brilliancy,  falling  off  to  become  invisi- 
ble for  a  time  and  then  return  to  its  maximum  bright- 
ness after  an  interval  of  eleven  months  from  the  preceding 
maximum.  In  1901  it  should  reach  its  greatest  brilliancy 
about  midsummer,  and  a  month  earlier  than  this  for  each 


322  ASTRONOMY 

succeeding  year.  Find  it  by  means  of  the  star  map,  and 
by  comparing  its  brightness  from  night  to  night  with 
neighboring  stars  of  about  the  same  magnitude  see  how  it 
changes  with  respect  to  them. 

The  interval  of  time  from  maximum  to  maximum  of 
brightness — 331.6  days  for  Mira — is  called  the  star's  pe- 
riod, and  within  its  period  a  star  regularly  variable  runs 
through  all  its  changes  of  brilliancy,  much  as  the  weather 
runs  through  its  cycle  of  changes  in  the  period  of  a  year. 
But,  as  there  are  wet  years  and  dry  ones,  hot  years  and  cold, 
so  also  with  variable  stars,  many  of  them  show  differences 
more  or  less  pronounced  between  different  periods,  and 
one  such  difference  has  already  been  noted  in  the  case  of 
Mira ;  its  maximum  brilliancy  is  different  in  different  years. 
So,  too,  the  length  of  the  period  fluctuates  in  many  cases, 
as  does  every  other  circumstance  connected  with  it,  and 
predictions  of  what  such  a  variable  star  will  do  are  notori- 
ously unreliable. 

205.  The  Algol  variables. — On  the  other  hand,  some  vari- 
able stars  present  an  almost  perfect  regularity,  repeating 
their  changes  time  after  time  with  a  precision  like  that  of 
clockwork.  Algol  is  one  type  of  these  regular  variables, 
having  a  period  of  68.8154  hours,  during  six  sevenths  of 
which  time  it  shines  with  unchanging  luster  as  a  star  of 
the  2.3  magnitude,  but  during  the  remaining  9  hours  of 
each  period  it  runs  down  to  the  3.5  magnitude,  and  comes 
back  again,  as  is  shown  by  a  curve  in  Fig.  130.  The  horizon- 
tal scale  here  represents  hours,  reckoned  from  the  time  of 
the  star's  minimum  brightness,  and  the  vertical  scale  shows 
stellar  magnitudes.  Such  a  diagram  is  called  the  star's 
light  curve,  and  we  may  read  from  it  that  at  any  time  be- 
tween 5h.  and  32h.  after  the  time  of  minimum  the  star's 
magnitude  is  2.32;  at  2h.  after  a  minimum  the  magni- 
tude is  2.88,  etc.  What  is  the  magnitude  an  hour  and  a 
half  before  the  time  of  minimum  ?  What  is  the  magnitude 
43  days  after  a  minimum  ? 


THE  FIXED  STARS 


323 


The  arrows  shown  in  Fig.  130  are  a  feature  not  usually 
found  with  light  curves,  but  in  this  case  each  one  repre- 
sents a  spectroscopic  determination  of  the  motion  of  Algol 
in  the  line  of  sight.  These  observations  extended  over  a 


FIG.  130.— The  light  curve  of  Algol. 

period  of  more  than  two  years,  but  they  are  plotted  in  the 
figure  with  reference  to  the  number  of  hours  each  one  pre- 
ceded or  followed  a  minimum  of  the  star's  light,  and  each 
arrow  shows  not  only  the  direction  of  the  star's  motion 
along  the  line  of  sight,  the  arrows  pointing  down  denoting 
approach  of  the  star  toward  the  earth,  but  also  its  velocity, 
each  square  of  the  ruling  corresponding  to  10  kilometers 
(6.2  miles  per  second).  The  differences  of  velocity  shown 
by  adjacent  arrows  come  mainly  from  errors  of  observation 
and  furnish  some  idea  of  how  consistent  among  themselves 
such  observations  are,  but  there  can  be  no  doubt  that  before 
minimum  the  star  is  moving  away  from  the  earth,  and  after 
minimum  is  approaching  it.  It  is  evident  from  these  ob- 
servations that  in  Algol  we  have  to  do  with  a  spectroscopic 
binary,  one  of  whose  components  is  a  dark  star  which,  once 
in  each  revolution,  partially  eclipses  the  bright  star  and 
produces  thus  the  variations  in  its  light.  By  combining 
the  spectroscopic  observations  with  the  variations  in  the 
star's  light,  Vogel  finds  that  the  bright  star,  Algol,  itself 
has  a  diameter  somewhat  greater  than  that  of  the  sun,  but 


324: 


ASTRONOMY 


is  of  low  density,  so  that  its  mass  is  less  than  half  that  of 
the  sun,  while  the  dark  star  is  a  very  little  smaller  than  the 
sun  and  has  about  a  quarter  of  its  mass.  The  distance  be- 
tween the  two  stars,  dark  and  bright,  is  3,200,000  miles. 
Fig.  129,  which  is  drawn  to  scale,  shows  the  relative  posi- 
tions and  sizes  of  these  stars  as  well  as  the  orbits  in  which 
they  move. 

The  mere  fact  already  noted  that  close  binary  systems 
exist  in  considerable  numbers  is  sufficient  to  make  it 
probable  that  a  certain  proportion  of  these  stars  would 
have  their  orbit  planes  turned  so  nearly  edgewise  toward 
the  earth  as  to  produce  eclipses,  and  corresponding  to  this 
probability  there  are  already  known  no  less  than  15  stars  of 
the  Algol  type  of  eclipse  variables,  and  only  a  beginning 
has  been  made  in  the  search  for  them. 

206.  Variables  of  the  (3  Lyrse  type. — In  addition  to  these 
there  is  a  certain  further  number  of  binary  variables  in 
which  both  components  are  bright  and  where  the  varia- 
tion of  brightness  follows  a  very  different  course.  Capella 


Days 


FIG.  131.— The  light  curve  of  0  Lyrse. 


would  be  such  a  variable  if  its  orbit  plane  were  directed 
exactly  toward  the  earth,  and  the  fact  that  its  light  is  not 
variable  shows  conclusively  that  such  is  not  the  position  of 
the  orbit.  Fig.  131  represents  the  light  curve  of  one  of  the 


THE  FIXED  STARS  325 

best-known  variable  systems  of  this  second  type,  that  of 
/?  Lyrse,  whose  period  is  12  days  21.8  hours,  and  the  student 
should  read  from  the  curve  the  magnitude  of  the  star  for 
different  times  during  this  interval.  According  to  Myers, 
this  light  curve  and  the  spectroscopic  observations  of  the 
star  point  to  the  existence  of  a  binary  star  of  very  remark- 
able character,  such  as  is  shown,  together  with  its  orbit  and 
a  scale  of  miles,  in  Fig.  132.  Note  the  tide  which  each  of 


To  the  Earth 


10,000,000  miles 

FIG.  132.— The  system  of  /3  Lyrae.— MYERS. 

these  stars  raises  in  the  other,  thus  changing  their  shapes 
from  spheres  into  ellipsoids.  The  astonishing  dimensions 
of  these  stars  are  in  part  compensated  by  their  very  low 
density,  which  is  less  than  that  of  air,  so  that  their  masses 
are  respectively  only  10  times  and  21  times  that  of  the 
sun  !  But  these  dimensions  and  masses  perhaps  require 
confirmation,  since  they  depend  upon  spectroscopic  obser- 
vations of  doubtful  interpretation.  In  Fig.  132  what  rela- 
tive positions  must  the  stars  occupy  in  their  orbit  in  order 
that  their  combined  light  should  give  ft  Lyrae  its  maxi- 
mum brightness  ?  What  position  will  furnish  a  minimum 
brightness  ? 

207.  Variables  of  long  and  short  periods, — It  must  not  be 
supposed  that  all  variable  stars  are  binaries  which  eclipse 
each  other.  By  far  the  larger  part  of  them,  like  Mira,  are 
not  to  be  accounted  for  in  this  way,  and  a  distinction  which 


326  ASTRONOMY 

is  pretty  well  marked  in  the  length  of  their  periods  is  sig- 
nificant in  this  connection.  There  is  a  considerable  num- 
ber of  variable  stars  with  periods  shorter  than  a  month,  and 
there  are  many  having  periods  longer  than  6  months,  but 
there  are  very  few  having  periods  longer  than  18  months, 
or  intermediate  between  1  month  and  6  months,  so  that  it 
is  quite  customary  to  divide  variable  stars  into  two  classes 
— those  of  long  period,  6  months  or  more,  and  those  of 
short  period  less  than  6  months,  and  that  this  distinction 
corresponds  to  some  real  difference  in  the  stars  themselves 
is  further  marked  by  the  fact  that  the  long-period  variables 
are  prevailingly  red  in  color,  while  the  short-period  stars 
are  almost  without  exception  white  or  very  pale  yellow. 
In  fact,  the  longer  the  period  the  redder  the  star,  although 
it  is  not  to  be  inferred  that  all  red  stars  are  variable ;  a 
considerable  percentage  of  them  shine  with  constant  light. 
The  eclipse  explanation  of  variability  holds  good  only  for 
short-period  variables,  and  possibly  not  for  all  of  them, 
while  for  the  long-period  variables  there  is  no  explanation 
which  commands  the  general  assent  of  astronomers,  al- 
though unverified  hypotheses  are  plenty. 

The  number  of  stars  known  to  be  variable  is  about  400, 
while  a  considerable  number  of  others  are  "suspected," 
and  it  would  not  be  surprising  if  a  large  fraction  of  all  the 
stars  should  be  found  to  fluctuate  a  little  in  brightness. 
The  sun's  spots  may  suffice  to  make  it  a  variable  star  with 
a  period  of  11  years. 

The  discovery  of  new  variables  is  of  frequent  occur- 
rence, and  may  be  expected  to  become  more  frequent  when 
the  sky  is  systematically  explored  for  them  by  the  ingen- 
ious device  suggested  by  Pickering  and  illustrated  in  Fig. 
133.  A  given  region  of  the  sky— e.  g.,  the  Northern  Crown 
— is  photographed  repeatedly  upon  the  same  plate,  which  is 
shifted  a  little  at  each  new  exposure,  so  that  the  stars  shall 
fall  at  new  places  upon  it.  The  finally  developed  plate 
shows  a  row  of  images  corresponding  to  each  star,  and  if 


THE  FIXED  STARS 


327 


the  star's  light  is  constant  the  images  in  any  given  row  will 
all  be  of  the  same  size,  as  are  most  of  those  in  Fig.  133 ; 
but  a  variable  star  such  as  is  shown  by  the  arrowhead 
reveals  its  presence  by  the  broken  aspect  of  its  row  of 


..•* 


FIG.  133. — Discovery  of  a  variable  star  by  means  of  photography. — PICKERING. 

dots,  a  minimum  brilliancy  being  shown  by  smaller  and  a 
maximum  by  larger  ones.  In  this  particular  case,  at  two 
exposures  the  star  was  too  faint  to  print  its  image  upon 
the  plate. 

208.  New  stars. — Next  to  the  variable  stars  of  very  long 
or  very  irregular  period  stand  the  so-called  new  or  tempo- 
rary stars,  which  appear  for  the  most  part  suddenly,  and 
after  a  brief  time  either  vanish  altogether  or  sink  to  com- 
parative insignificance.  These  were  formerly  thought  to 
be  very  remarkable  and  unusual  occurrences — "  the  birth 
of  a  new  world  " — and  it  is  noteworthy  that  no  new  star 
is  recorded  to  have  been  seen  from  1670  to  1848  A.  D.,  for 
since  that  time  there  have  been  no  less  than  four  of  them 


328  ASTRONOMY 

visible  to  the  naked  eye  and  others  telescopic.  In  so  far 
as  these  new  stars  are  not  ordinary  variables  (Mira,  first 
seen  in  1596,  was  long  counted  as  a  new  star),  they  are  com- 
monly supposed  due  to  chance  encounters  between  stars 
or  other  cosmic  bodies  moving  with  considerable  velocities 
along  orbits  which  approach  very  close  to  each  other.  The 
actual  collision  of  two  dark  bodies  moving  with  high  ve- 
locities is  clearly  sufficient  to  produce  a  luminous  star — 
e.  g.,  meteors — and  even  the  close  approach  of  two  cooled- 
off  stars,  might  result  in  tidal  actions  which  would  rend 
open  their  crusts  and  pour  out  the  glowing  matter  from 
within  so  as  to  produce  temporarily  a  very  great  accession 
of  brightness. 

The  most  famous  of  all  new  stars  is  that  which,  accord- 
ing to  Tycho  Brahe's  report,  appeared  in  the  year  1572,  and 
was  so  bright  when  at  its  best  as  to  be  seen  with  the  naked 
eye  in  broad  daylight.  It  continued  visible,  though  with 
fading  light,  for  about  16  months,  and  finally  disappeared 
to  the  naked  eye,  although  there  is  some  reason  to  suppose 
that  it  can  be  identified  with  a  ruddy  star  of  the  eleventh 
magnitude  in  the  constellation  Cassiopeia,  whose  light  still 
shows  traces  of  variability. 

No  modern  temporary  star  approaches  that  of  Tycho 
in  splendor,  but  in  some  respects  the  recent  ones  surpass 
it  in  interest,  since  it  has  been  possible  to  apply  the  spec- 
troscope to  the  analysis  of  their  light  and  to  find  thereby 
a  much  more  complex  set  of  conditions  in  the  star  than 
would  have  been  suspected  from  its  light  changes  alone. 
The  temporary  star  which  appeared  in  the  constellation 
Auriga  in  December,  1891,  disappeared  in  April,  1892,  and 
three  months  later  reappeared  for  another  season,  is  the 
most  remarkable  of  recent  temporary  stars,  and  presents 
many  anomalies  for  which  no  entirely  satisfactory  expla- 
nation has  yet  been  found.  Its  spectrum  contained  both 
dark  and  bright  lines,  apparently  due  to  the  same  chemical 
substances,  but  displaced  toward  opposite  ends  of  the  spec- 


THE  FIXED  STARS  329 

trum,  as  if  they  came  from  different  bodies  moving  past 
each  other  with  velocities  to  be  measured  in  hundreds  of 
miles  per  second.  In  character  the  lines,  chiefly  those  of 
hydrogen  and  iron,  suggested  at  one  time  the  sun's  chro- 
mosphere, at  another  the  conditions  which  obtain  in  neb- 
ulas (Chapter  XI V),  and  the  only  conclusion  regarding  it 
upon  which  there  seems  to  be  a  substantial  agreement  is 
that  in  producing  and  reviving  the  temporary  brightness 
of  this  star  at  least  two  and  possibly  several  independent 
bodies  were  involved,  although  even  this  is  not  altogether 
certain. 


CHAPTER  XIV 

STARS   AND   NEBULJB 

209.  Stellar  colors,— We  have  already  seen  that  one  star 
differs  from  another  in  respect  of  color  as  well  as  bright- 
ness, and  the  diligent  student  of  the  sky  will  not  fail  to 
observe  for  himself  how  the  luster  of  Sirius  and  Rigel  is 
more  nearly  a  pure  white  than  is  that  of  any  other  stars  in 
the  heavens,  while  at  the  other  end  of  the  scale  a  Orionis 
and  Aldebaran  are  strongly  ruddy,  and  Antares  presents  an 
even  deeper  tone  of  red.  Between  these  extremes  the 
light  of  every  star  shows  a  mixture  of  the  rainbow  hues,  in 
which  a  very  pale  yellow  is  the  predominant  color,  shading 
off,  as  we  have  seen,  to  white  at  one  end  of  the  scale  and 
red  at  the  other.  There  are  no  green  stars,  or  blue  stars, 
or  violet  stars,  save  in  one  exceptional  class  of  cases — viz., 
where  the  two  components  of  a  double  star  are  of  very  dif- 
ferent brightness,  it  is  quite  the  usual  thing  for  them  to 
have  different  colors,  and  then,  almost  without  exception, 
the  color  of  the  fainter  star  lies  nearer  to  the  violet  end 
of  the  spectrum  than  does  the  color  of  the  bright  one, 
and  sometimes  shows  a  distinctly  blue  or  green  hue.  A 
fine  type  of  such  double  star  is  ft  Cygni,  in  which  the 
components  are  respectively  yellow  and  blue,  and  the  yel- 
low star  furnishes  eight  times  as  much  light  as  the  blue 
one. 

The  exception  which  double  stars  thus  make  to  the  gen- 
eral rule  of  stellar  colors,  yellow  and  red,  but  no  color  of 
shorter  wave  length,  has  never  been  satisfactorily  explained, 
330 


STARS  AND  NEBULA  331 

but  the  rule  itself  presents  no  difficulties.  Each  star  is  an 
incandescent  body,  giving  off  radiant  energy  of  every  wave 
length  within  the  limits  of  the  visible  spectrum,  and,  in- 
deed, far  beyond  these  limits.  If  this  radiant  energy  could 
come  unhindered  to  our  eyes  every  star  would  appear  white, 
but  they  are  all  surrounded  by  atmospheres — analogous  to 
the  chromosphere  and  reversing  layer  of  the  sun — which 
absorb  a  portion  of  their  radiant  energy  and,  like  the  earth's 
atmosphere,  take  a  heavier  toll  from  the  violet  than  from 
the  red  end  of  the  spectrum.  The  greater  the  absorption 
in  the  star's  atmosphere,  therefore,  the  feebler  and  the  rud- 
dier will  be  its  light,  and  corresponding  to  this  the  red  stars 
are  as  a  class  fainter  than  the  white  ones. 

210.  Chemistry  of  the  stars,— The  spectroscope  is  pre-em- 
inently the  instrument  to  deal  with  this  absorption  of  light 
in  the  stellar  atmospheres,  just  as  it  deals  with  that  absorp- 
tion in  the  sun's  atmosphere  to  which  are  due  the  dark  lines 
of  the  solar  spectrum,  although  the  faiiitness  of  starlight, 
compared  with  that  of  the  sun,  presents  a  serious  obstacle 
to  its  use.  Despite  this  difficulty  most  of  the  lucid  stars 
and  many  of  the  telescopic  ones  have  been  studied  with 
the  spectroscope  and  found  to  be  similar  to  the  sun  and 
the  earth  as  respects  the  material  of  which  they  are  made. 
Such  familiar  chemical  elements  as  hydrogen  and  iron,  car- 
bon, sodium,  and  calcium  are  scattered  broadcast  through- 
out the  visible  universe,  and  while  it  would  be  unwarranted 
by  the  present  state  of  knowledge  to  say  that  the  stars  con- 
tain nothing  not  found  in  the  earth  and  the  sun,  it  is  evi- 
dent that  in  a  broad  way  their  substance  is  like  rather  than 
unlike  that  composing  the  solar  system,  and  is  subject  to 
the  same  physical  and  chemical  laws  which  obtain  here. 
Galileo  and  Kewton  extended  to  the  heavens  the  terrestrial 
sciences  of  mathematics  and  mechanics,  but  it  remained  to 
the  nineteenth  century  to  show  that  the  physics  and  chem- 
istry of  the  sky  are  like  the  physics  and  chemistry  of  the 
earth. 


332  ASTRONOMY 

211.  Stellar  spectra, — When  the  spectra  of  great  numbers 
of  stars  are  compared  one  with  another,  it  is  found  that 
they  bear  some  relation  to  the  colors  of  the  stars,  as,  indeed, 
we  should  expect,  since  spectrum  and  color  are  both  pro- 
duced by  the  stellar  atmospheres,  and  it  is  found  useful  to 
classify  these  spectra  into  three  types,  as  follows : 

Type  I.  Sirian  stars. — Speaking  generally,  the  stars 
which  are  white  or  very  faintly  tinged  with  yellow,  furnish 
spectra  like  that  of  Sirius,  from  which  they  take  their 
name,  or  that  of  (3  Aurigse  (Fig.  124),  which  is  a  continuous 
spectrum,  especially  rich  in  energy  of  short  wave  length — 
i.  e.,  violet  and  ultra-violet  light,  and  is  crossed  by  a  rela- 
tively small  number  of  heavy  dark  lines  corresponding  to 
the  spectrum  of  hydrogen.  Sometimes,  however,  these  lines 
are  much  fainter  than  is  here  shown,  and  we  find  associated 
with  them  still  other  faint  ones  pointing  to  the  presence  of 
other  metallic  substances  in  the  star's  atmosphere.  These 
metallic  lines  are  not  always  present,  and  sometimes  even 
the  hydrogen  lines  themselves  are  lacking,  but  the  spectrum 
is  always  rich  in  violet  and  ultra-violet  light. 

Since  with  increasing  temperature  a  body  emits  a  con- 
tinually increasing  proportion  of  energy  of  short  wave 
length  (§  118),  the  richness  of  these  spectra  in  such  energy 
points  to  a  very  high  temperature  in  these  stars,  probably 
surpassing  in  some  considerable  measure  that  of  the  sun. 
Stars  with  this  type  of  spectrum  are  more  numerous  than 
all  others  combined,  but  next  to  them  in  point  of  numbers 
stands — 

Type  II.  Solar  stars. — To  this  type  of  spectrum  belong 
the  yellow  stars,  which  show  spectra  like  that  of  the  sun, 
or  of  Pollux  (Fig.  125).  These  are  not  so  rich  in  violet 
light  as  are  those  of  Type  I,  but  in  complexity  of  spectrum 
and  in  the  number  of  their  absorption  lines  they  far  sur- 
pass the  Sirian  stars.  They  are  supposed  to  be  at  a  lower 
temperature  than  the  Sirian  stars,  and  a  much  larger  num- 
ber of  chemical  elements  seems  present  and  active  in  the 


STARS  AND  NEBULAE  333 

reversing  layer  of  their  atmospheres.  The  strong  resem- 
blance which  these  spectra  bear  to  that  of  the  sun,  together 
with  the  fact  that  most  of  the  sun's  stellar  neighbors  have 
spectra  of  this  type,  justify  us  in  ranking  both  them  and  it 
as  members  of  one  class,  called  solar  stars. 

Type  III.  Red  stars. — A  small  number  of  stars  show 
spectra  comparable  with  that  of  a  Herculis  (Fig.  134),  in 
which  the  blue  and  the  violet  part  of  the  spectrum  is  al- 
most obliterated,  and  the  remaining  yellow  and  red  parts 


FIG.  134.— The  spectrum  of  a  Herculis.— ESPIN. 

show  not  only  dark  lines,  but  also  numerous  broad  dark 
bands,  sharp  at  one  edge,  and  gradually  fading  out  at  the 
other.  It  is  this  selective  absorption,  extinguishing  the  blue 
and  leaving  the  red  end  of  the  spectrum,  which  produces 
the  ruddy  color  of  these  stars,  while  the  bands  in  their 
spectra  "  are  characteristic  of  chemical  combinations,  and 
their  presence  .  .  .  proves  that  at  certain  elevations  in  the 
atmospheres  of  these  stars  the  temperature  has  sunk  so  low 
that  chemical  combinations  can  be  formed  and  maintained  " 
(Scheiner-Frost).  One  of  the  chemical  compounds  here  in- 
dicated is  a  hydrocarbon  similar  to  that  found  in  comets. 
In  the  white  and  yellow  stars  the  temperatures  are  so  high 
that  the  same  chemical  elements,  although  present,  can  not 
unite  one  with  another  to  form  compound  substances. 

Most  of  the  variable  stars  are  red  and  have  spectra  of 
the  third  type  ;  but  this  does  not  hold  true  for  the  eclipse 
variables  like  Algol,  all  of  which  are  white  stars  with  spec- 
tra of  the  first  type.  The  ordinary  variable  star  is  there- 
fore one  with  a  dense  atmosphere  of  relatively  low  tempera- 
ture  and  complex  structure,  which  produces  the  prevailing 
red  color  of  these  stars  by  absorbing  the  major  part  of 


334  ASTRONOMY 

their  radiant  energy  of  short  wave  length  while  allowing 
the  longer,  red  waves  to  escape.  Although  their  exact 
nature  is  not  understood,  there  can  be  little  doubt  that  the 
fluctuation  in  the  light  of  these  stars  is  due  to  processes 
taking  place  within  the  star  itself,  but  whether  above  or 
below  its  photosphere  is  still  uncertain. 

212.  Classes  of  stars, — There  is  no  hard-and-fast  dividing 
line  between  these  types  of  stellar  spectra,  but  the  change 
from  one  to  another  is  by  insensible  gradations,  like  the 
transition  from  youth  to  manhood  and  from  manhood  to 
old  age,  and  along  the  line  of  transition  are  to  be  found 
numberless  peculiarities  and  varieties  of  spectra  not  enu- 
merated above — e.  g.,  a  few  stars  show  not  only  dark  absorp- 
tion lines  in  their  spectra  but  bright  lines  as  well,  which, 
like  those  in  Fig.  48,  point  to  the  presence  of  incandescent 
vapors,  even  in  the  outer  parts  of  their  atmospheres.    Among 
the  lucid  stars  about  75  per  cent  have  spectra  of  the  first 
type,  23  per  cent  are  of  the  second  type,  1  per  cent  of  the 
third  type,  and  the  remaining  1  per  cent  are  peculiar  or  of 
doubtful  classification.     Among  the  telescopic  stars  it  is 
probable  that  much  the  same  distribution  holds,  but  in  the 
present  state  of  knowledge  it  is  not  prudent  to  speak  with 
entire  confidence  upon  this  point. 

That  the  great  number  of  stars  whose  spectra  have  been 
studied  should  admit  of  a  classification  so  simple  as  the 
above,  is  an  impressive  fact  which,  when  supplemented  by 
the  further  fact  of  a  gradual  transition  from  one  type  of 
spectrum  to  the  next,  leaves  little  room  for  doubt  that  in 
the  stars  we  have  an  innumerable  throng  of  individuals  be- 
longing to  the  same  species  but  in  different  stages  of  devel- 
opment, and  that  the  sun  is  only  one  of  these  individuals, 
of  something  less  than  medium  size  and  in  a  stage  of  de- 
velopment which  is  not  at  all  peculiar,  since  it  is  shared  by 
nearly  a  fourth  of  all  the  stars. 

213.  Star  clusters. — In  previous  chapters  we  have  noted 
the  Pleiades  and   Prsesepe  as  star  clusters  visible  to  the 


STARS  AND  NEBULAE 


335 


FIG.  135.— Star  cluster  in  Hercules. 


naked  eye,  and  to  them  we  may  add  the  Hyades,  near  Aldeb- 
aran,  and  the  little  constellation  Coma  Berenices.  But 
more  impressive  than  any  of  these,  although  visible  only 
in  a  telescope,  is  the  splendid  cluster  in  Hercules,  whose 
appearance  in  a  tele- 
scope of  moderate  size 
is  shown  in  Fig.  135, 
while  Fig.  136  is  a  pho- 
tograph of  the  same 
cluster  taken  with  a 
very  large  reflecting 
telescope.  This  is  only 
a  type  of  many  tele- 
scopic clusters  which 
are  scattered  over  the 
sky,  and  which  are  made 
up  of  stars  packed  so 
closely  together  as  to  become  indistinguishable,  one  from 
another,  at  the  center  of  the  cluster.  Within  an  area 
which  could  be  covered  by  a  third  of  the  full  moon's  face 
are  crowded  in  this  cluster  more  than  five  thousand  stars 
which  are  unquestionably  close  neighbors,  but  whose  ap- 
parent nearness  to  each  other  is  doubtless  due  to  their 
great  distance  from  us.  It  is  quite  probable  that  even  at 
the  center  of  this  cluster,  where  more  than  a  thousand  stars 
are  included  within  a  radius  of  160",  the  actual  distances 
separating  adjoining  stars  are  much  greater  than  that  sepa- 
rating earth  and  sun,  but  far  less  than  that  separating  the 
sun  from  its  nearest  stellar  neighbor. 

An  interesting  discovery  of  recent  date,  made  by  Pro- 
fessor Bailey  in  photographing  star  clusters,  is  that  some 
few  of  them,  which  are  especially  rich  in  stars,  contain  an 
extraordinary  number  of  variable  stars,  mostly  very  faint 
and  of  short  period.  Two  clusters,  one  in  the  northern  and 
one  in  the  southern  hemisphere,  contain  each  more  than  a 
hundred  variables,  and  an  even  more  extraordinary  case  is 


336  ASTRONOMY 

presented  by  a  cluster,  called  Messier  5,  not  far  from  the 
star  a  Serpentis,  which  contains  no  less  than  sixty-three 
variables,  all  about  of  the  fourteenth  magnitude,  all  having 
light  periods  which  differ,  but  little  from  half  a  day,  all 


FIG.  136. — Star  cluster  in  Hercules. — KEELER. 

having  light  curves  of  about  the  same  shape,  and  all  having 
a  range  of  brightness  from  maximum  to  minimum  of  about 
one  magnitude.  An  extraordinary  set  of  coincidences 
which  "points  unmistakably  to  a  common  origin  and  cause 
of  variability." 


STARS  AND  NEBULAE  337 

214.  Nebulae, — Returning  to  Fig.  136,  we  note  that  its 
background  has  a  hazy  appearance,  and  that  at  its  center 


FIG.  137.— The  Andromeda  nebula  as  seen  in  a  very  small  telescope. 

the  stars  can  no  longer  be  distinguished,  but  blend  one 
with  another  so  as  to  appear  like  a  bright  cloud.     The 


FIG.  138.— The  Andromeda  nebula  and  Holmes's  comet. 
Photographed  by  BARNARD. 


338  ASTRONOMY 

outer  part  of  the  cluster  is  resolved  into  stars,  while  in  the 
picture  the  inner  portion  is  not  so  resolved,  although  in 


FIG.  139.— A  drawing  of  the  Andromeda  nebula. 

the  original  photographic  plate  the  individual  stars  can  be 
distinguished  to  the  very  center  of  the  cluster.     In  many 


FIG.  140.— A  photograph  of  the  Andromeda  nebula.— ROBERTS. 


STARS  AND  NEBULA 


339 


cases,  however,  this  is  not  possible,  and  we  have  an  irre- 
solvable duster  which  it  is  customary  to  call  a  nebula 
(Latin,  little  cloud). 

The  most  conspicuous  example  of  this  in  the  northern 
heavens  is  the  great  nebula  in  Andromeda  (R.  A.  Oh  37m, 
Dec.  +  41°),  which  may  be  seen  with  the  naked  eye  as  a 
faint  patch  of  foggy  light.  Look  for  it.  This  appears  in 
an  opera  glass  or  very  small  telescope  not  unlike  Fig.  137, 
which  is  reproduced  from  a  sketch.  Fig.  138  is  from  a 
photograph  of  the  same  object  showing  essentially  the  same 
shape  as  in  the  preceding  figure,  but  bringing  out  more 
detail.  Note  the  two  small  nebulae  adjoining  the  large 
one,  and  at  the  bottom  of  the  picture  an  object  which  might 
easily  be  taken  for  another  nebula  but  which  is  in  fact 
a  tailless  comet  that  chanced  to  be  passing  that  part  of 
the  sky  when  the  picture  was  taken.  Fig.  139  is  from  an- 
other drawing  of  this  nebula, 
although  it  is  hardly  to  be 
recognized  as  a  representa- 
tion of  the  same  thing;  but 
its  characteristic  feature,  the 
two  dark  streaks  near  the  cen- 
ter of  the  picture,  is  justified 
in  part  by  Fig.  140,  which  is 
from  a  photograph  made  with 
a  large  reflecting  telescope. 

A  comparison  of  these  sev- 
eral representations  of  the 
same  thing  will  serve  to  illus- 
trate the  vagueness  of  its  out- 
lines, and  how  much  the  im- 
pressions to  be  derived  from 
nebulae  depend  upon  the  tele- 
scopes employed  and  upon  the 

observer's  own  prepossessions.  The  differences  among  the 
pictures  can  not  be  due  to  any  change  in  the  nebula  itself, 


FIG.  141.— Types  of  nebulae. 


34:0  ASTRONOMY 

for  half  a  century  ago  it  was  sketched  much  as  shown  in 
the  latest  of  them  (Fig.  140). 

215.  Typical  nebulae. — Some  of  the  fantastic  forms  which 
nebulae  present  in  the  telescope  are  shown  on  a  small  scale 
in  Fig.  141,  but  in  recent  years  astronomers  have  learned  to 


FIG.  142.— The  Trifld  nebula.— KEELER. 


place  little  reliance  upon  drawings  such  as  these,  which  are 
now  almost  entirely  supplanted  by  photographs  made  with 
long  exposures  in  powerful  telescopes.  One  of  the  most 
exquisite  of  these  modern  photographs  is  that  of  the  Trifid 


STARS  AND  NEBULA 


341 


nebula  in  Sagittarius  (Fig.  142).  Note  especially  the  dark 
lanes  that  give  to  this  nebula  its  name,  Trifid,  and  which  run 
through  its  brightest  parts,  breaking  it  into  seemingly  inde- 
pendent sections.  The  area  of  the  sky  shown  in  this  cut  is 
about  15  per  cent  less  than  that  covered  by  the  full  moon. 


FIG.  143.— A  nebula  in  Cygnus.— KEELER. 

Fig.  143  shows  a  very  different  type  of  nebula,  found  in 
the  constellation  Cygnus,  which  appears  made  up  of  fila- 
ments closely  intertwined,  and  stretches  across  the  sky  for 
a  distance  considerably  greater  than  the  moon's  diameter. 


342 


ASTRONOMY 


A  much  smaller  but  equally  striking  nebula  is  that  in 
the  constellation  Canes  Venatici  (Fig.  144),  which  shows  a 
most  extraordinary  spiral  structure,  as  if  the  stars  compos- 
ing it  were  flowing  in  along  curved  lines  toward  a  center  of 
condensation.  The  diameter  of  the  circular  part  of  this 


FIG.  144.— Spiral  nebula  in  Canes  Venatici.— KEELER. 

nebula,  omitting  the  "projection  toward  the  bottom  of  the 
picture,  is  about  five  minutes  of  arc,  a  sixth  part  of  the 
diameter  of  the  moon,  and  its  thickness  is  probably  very 
small  compared  with  its  breadth,  perhaps  not  much  exceed- 


STARS  AND  NEBULA  343 

ing  the  width  of  the  spiral  streams  which  compose  it.  Note 
how  the  bright  stars  that  appear  within  the  area  of  this 
nebula  fall  on  the  streams  of  nebulous  matter  as  if  they 
were  part  of  them.  This  characteristic  grouping  of  the 
stars,  which  is  followed  in  many  other  nebulas,  shows  that 


FIG.  145.— Great  nebula  about  the  e tar  p  Ophiuchi.— BARNARD. 

they  are  really  part  and  parcel  of  the  nebula  and  not  merely 
on  line  with  it.  Fig.  145  shows  how  a  great  nebula  is  asso- 
ciated with  the  star  p  Ophiuchi. 

Probably  the  most  impressive  of  all  nebulae  is  the  great 
one  in  Orion  (Fig.  146),  whose  position  is  shown  on  the 
star  map  between  Eigel  and  £  Orionis.  Look  for  it  with 
an  opera  glass  or  even  with  the  unaided  eye.  This  is  some- 
times called  an  amorphous — i.  e.,  shapeless — nebula,  because 
it  presents  no  definite  form  which  the  eye  can  grasp  and 
little  trace  of  structure  or  organization.  It  is  "without 
form  and  void  "  at  least  in  its  central  portions,  although  on 
its  edges  curved  filaments  may  be  traced  streaming  away 


344  ASTRONOMY 

from  the  brighter  parts  of  the  central  region.  This  nebula, 
as  shown  in  Fig.  146,  covers  an  area  about  equal  to  that  of 
the  full  moon,  without  counting  as  any  part  of  this  the 
companion  nebula  shown  at  one  side,  but  photographs 
made  with  suitable  exposures  show  that  faint  outlying  parts 
of  the  nebula  extend  in  curved  lines  over  the  larger  part  of 


FIG.  146.— The  Orion  nebula. 


the  constellation  Orion.  Indeed,  over  a  large  part  of  the 
entire  sky  the  background  is  faintly  covered  with  nebulous 
light  whose  brighter  portions,  if  each  were  counted  as  a 
separate  nebula,  would  carry  the  total  number  of  such  ob- 
jects well  into  the  hundreds  of  thousands. 

The  Pleiades  (Plate  IV)  present  a  case  of  a  resolvable 
star  cluster  projected  against  such  a  nebulous  background 
whose  varying  intensity  should  be  noted  in  the  figure.  A 
part  of  this  nebulous  matter  is  shown  in  wisps  extending 
from  one  star  to  the  next,  after  the  fashion  of  a  bridge,  and 
leaving  little  doubt  that  the  nebula  is  actually  a  part  of  the 
cluster  and  not  merely  a  background  for  it. 

Fig.  147  shows  a  series  of  so-called  double  nebulae  per- 
haps comparable  with  double  stars,  although  the  most 
recent  photographic  work  seems  to  indicate  that  they  are 


• 


STARS  AND  NEBULA 


345 


really  faint  spiral  nebulae  in  which  only  the  brightest  parts 
are  shown  by  the  telescope. 

According  to  Keeler,  the  spiral  is  the  prevailing  type 
of  nebulae,  and  while  Fig.  144  presents  the  most  perfect  ex- 
ample of  such  a  nebula,  the 
student  should  not  fail  to 
note  that  the  Andromeda  neb- 
ula (Fig.  140)  shows  distinct 
traces  of  a  spiral  structure, 
only  here  we  do  not  see  its 
true  shape,  the  nebula  being 
turned  nearly  edgewise  toward 
us  so  that  its  presumably  cir- 
cular outline  is  foreshortened 
into  a  narrow  ellipse. 

Another  type  of  nebula  of 
some  consequence  presents  in 
the  telescope  round  disks  like 
those  of  Uranus  or  Xeptune, 
and  this  appearance  has  given 
them  the  name  planetary  neb- 

iilce.  The  comet  in  Fig.  138,  if  smaller,  would  represent 
fairly  well  the  nebulae  of  this  type.  Sometimes  a  planetary 
nebula  has  a  star  at  its  center,  arid  sometimes  it  appears 
hollow,  like  a  smoke  ring,  and  is  then  called  a  ring  nebula. 
The  most  famous  of  these  is  in  the  constellation  Lyra,  not 
far  from  Vega. 

216.  Spectra  of  nebulae.— A  star  cluster,  like  the  one  in 
Hercules,  shows,  of  course,  stellar  spectra,  and  even  when 
irresolvable  the  spectrum  is  a  continuous  one,  testifying  to 
the  presence  of  stars,  although  they  stand  too  close  to- 
gether to  be  separately  seen.  But  in  a  certain,  number  of 
nebulae  the  spectrum  is  altogether  different,  a  discontinu- 
ous one  containing  only  a  few  bright  lines,  showing  that 
here  the  nebular  light  comes  from  glowing  gases  which 
are  subject  to  no  considerable  pressure.  The  planetary 


FIG.  147.— Double  nebulae. 
HERSCHEL. 


346  ASTRONOMY 

nebulae  all  have  spectra  of  this  kind  and  make  up  about 
half  of  all  the  known  gaseous  nebulae.  It  is  worthy  of 
note  that  a  century  ago  Sir  William  Herschel  had  observed 
a  green  shimmer  in  the  light  of  certain  nebulae  which  led 
him  to  believe  that  they  were  "  not  of  a  starry  nature,"  a 
conclusion  which  has  been  abundantly  confirmed  by  the 
spectroscope.  The  green  shimmer  is,  in  fact,  caused  by  a 
line  in  the  green  part  of  the  spectrum  that  is  always  pres- 
ent and  is  always  the  brightest  part  of  the  spectrum  of 
gaseous  nebulae. 

In  faint  nebulae  this  line  constitutes  the  whole  of  their 
visible  spectrum,  but  in  brighter  ones  two  or  three  other 
and  fainter  lines  are  usually  associated  with  it,  and  a  very 
bright  nebula,  like  that  in  Orion,  may  show  a  considerable 
number  of  extra  lines,  but  for  the  most  part  they  can  not 
be  identified  in  the  spectrum  of  any  terrestrial  substances. 
An  exception  to  this  is  found  in  the  hydrogen  lines,  which 
are  well  marked  in  most  spectra  of  gaseous  nebulae,  and 
there  are  indications  of  one  or  two  other  known  sub- 
stances. 

217.  Density  of  nebulae. — It  is  known  from  laboratory 
experiments  that  diminishing  the  pressure  to  which  an  in- 
candescent gas  is  subject,  diminishes  the  number  of  lines 
contained  in  its  spectrum,  and  we  may  surmise  from  the 
very  simple  character  and  few  lines  of  these  nebular  spec- 
tra that  the  gas  which  produces  them  has  a  very  small 
density.  But  this  is  far  from  showing  that  the  nebula 
itself  is  correspondingly  attenuated,  for  we  must  not  as- 
sume that  this  shining  gas  is  all  that  exists  in  the  nebula ; 
so  far  as  telescope  or  camera  are  concerned,  there  may  be 
associated  with  it  any  amount  of  dark  matter  which  can 
not  be  seen  because  it  sends  to  us  no  light.  It  is  easy 
to  think  in  this  connection  of  meteoric  dust  or  the  stuff  of 
which  comets  are  made,  for  these  seem  to  be  scattered 
broadcast  on  every  side  of  the  solar  system  and  may,  per- 
chance, extend  out  to  the  region  of  the  nebulae. 


STARS  AND  NEBULAE  347 

But,  whatever  may  be  associated  in  the  nebula  with  the 
glowing  gas  which  we  see,  the  total  amount  of  matter,  in- 
visible as  well  as  visible,  must  be  very  small,  or  rather  its 
average  density  must  be  very  small,  for  the  space  occupied 
by  such  a  nebula  as  that  of  Orion  is  so  great  that  if  the 
average  density  of  its  matter  were  equal  to  that  of  air  the 
resulting  mass  by  its  attraction  would  exert  a  sensible  effect 
upon  the  motion  of  the  sun  through  space.  The  brighter 
parts  of  this  nebula  as  seen  from  the  earth  subtend  an  angle 
of  about  half  a  degree,  and  while  we  know  nothing  of  its 
distance  from  us,  it  is  easy  to  see  that  the  farther  it  is  away 
the  greater  must  be  its  real  dimensions,  and  that  this  in- 
crease of  bulk  and  mass  with  increasing  distance  will  just 
compensate  the  diminishing  intensity  of  gravity  at  great 
distances,  so  that  for  a  given  angular  diameter — e.  g.,  half 
a  degree — the  force  with  which  this  nebula  attracts  the  sun 
depends  upon  its  density  but  not  at  all  upon  its  distance. 
Now,  the  nebula  must  attract  the  sun  in  some  degree,  and 
must  tend  to  move  it  and  the  planets  in  an  orbit  about 
the  attracting  center  so  that  year  after  year  we  should  see 
the  nebula  from  slightly  different  points  of  view,  and  this 
changed  point  of  view  should  produce  a  change  in  the  ap- 
parent direction  of  the  nebula  from  us — i.  e.,  a  proper  mo- 
tion, whose  amount  would  depend  upon  the  attracting  force, 
and  therefore  upon  the  density  of  the  attracting  matter. 
Observations  of  the  Orion  nebula  show  that  its  proper 
motion  is  wholly  inappreciable,  certainly  far  less  than  half 
a  second  of  arc  per  year,  and  corresponding  to  this  amount 
of  proper  motion  the  mean  density  of  the  nebula  must  be 
some  millions  of  times  (1010  according  to  Eanyard)  less  than 
that  of  air  at  sea  level— i.  e.,  the  average  density  throughout 
the  nebula  is  comparable  with  that  of  those  upper  parts 
of  the  earth's  atmosphere  in  which  meteors  first  become 
visible. 

218.  Motion  of  nebulae. — The  extreme  minuteness  of 
their  proper  motions  is  a  characteristic  feature  of  all 


348  ASTRONOMY 

nebulae.  Indeed,  there  is  hardly  a  known  case  of  sensible 
proper  motion  of  one  of  these  bodies,  although  a  dozen  or 
more  of  them  show  velocities  in  the  line  of  sight  ranging 
in  amount  from  -f-30  to  —40  miles  per  second,  the  plus 
sign  indicating  an  increasing  distance.  While  a  part  of 
these  velocities  may  be  only  apparent  and  due  to  the  mo- 
tion of  earth  and  sun  through  space,  a  part  at  least  is  real 
motion  of  the  nebulas  themselves.  These  seem  to  move 
through  the  celestial  spaces  in  much  the  same  way  and 


FIG.  148.— A  part  of  the  Milky  Way. 

with  the  same  velocities  as  do  the  stars,  and  their  smaller 
proper  motions  across  the  line  of  sight  (angular  motions) 
are  an  index  of  their  great  distance  from  us.  No  one  has 
ever  succeeded  in  measuring  the  parallax  of  a  nebula  or 
star  cluster. 

The  law  of  gravitation  presumably  holds  sway  within 
these  bodies,  and  the  fact  that  their  several  parts  and  the 
stars  which  are  involved  within  them,  although  attracted 
by  each  other,  have  shown  little  or  no  change  of  position 


STARS  AND  NEBULA 


349 


during  the  past  century,  is  further  evidence  of  their  low 
density  and  feeble  attraction.  In  a  few  cases,  however, 
there  seem  to  be  in  progress  within  a  nebula  changes  of 
brightness,  so  that  what  was  formerly  a  faint  part  has  be- 
come a  brighter  one,  or  vice  versa ;  but,  on  the  whole,  even 
these  changes  are  very  small. 

219.  The  Milky  Way.— Closely  related  to  nebulae  and 
star  clusters  is  another  feature  of  the  sky,  the  galaxy  or 
Milky  Way,  with  whose  appearance  to  the  unaided  eye  the 


FIG.  149.— The  Milky  Way  near  6  Ophiuchi.— BAUNARD. 

student  should  become  familiar  by  direct  study  of  the  thing 
itself.  Figs.  148  and  149  are  from  photographs  of  two 
small  parts  of  it,  and  serve  to  bring  out  the  small  stars  of 
which  it  is  composed.  Every  star  shown  in  these  pictures 
is  invisible  to  the  naked  eye,  although  their  combined  light 
is  easily  seen.  The  general  course  of  the  galaxy  across  the 
heavens  is  shown  in  the  star  maps,  but  these  contain  no 
indication  of  the  wealth  of  detail  which  even  the  naked  eye 
may  detect  in  it.  Bright  and  faint  parts,  dark  rifts  which 


350 


ASTRONOMY 


cut  it  into  segments,  here  and  there  a  hole  as  if  the  ribbon 
of  light  had  been  shot  away — such  are  some  of  the  features 
to  be  found  by  attentive  examination. 

Speaking  generally,  the  course  of  the  Milky  Way  is  a 
great  circle  completely  girdling  the  sky  and  having  its 
north  pole  in  the  constellation  Coma  Berenices.  The 
width  of  this  stream  of  light  is  very  different  in  different 
parts  of  the  heavens,  amounting  where  it  is  widest,  in  Lyra 
and  Cygnus,  to  something  more  than  30°,  although  its 
boundaries  are  too  vague  and  ill  denned  to  permit  much 
accuracy  of  measurement.  Observe  the  very  bright  part 
between  ft  and  y  Cygni,  nearly  opposite  Vega,  and  note 


FIG.  150.— The  Milky  Way  near  /3  Cygni.— BARNAKD. 

how  even  an  opera  glass  will  partially  resolve  the  nebulous 
light  into  a  great  number  of  stars,  which  are  here  rather 
brighter  than  in  other  parts  of  its  course.  But  the  resolu- 
tion into  stars  is  only  partial,  and  there  still  remains  a 
background  of  unresolved  shimmer.  Fig.  150  is  a  photo- 


STARS  AND  NEBULAE  351 

graph  of  a  small  part  of  this  region  in  which,  although 
each  fleck  of  light  represents  a  separate  star,  the  galaxy  is 
not  completely  resolved.  Compare  with  this  region,  rich 
in  stars,  the  nearly  empty  space  between  the  branches  of 
the  galaxy  a  little  west  of  Altair.  Another  hole  in  the 
Milky  Way  may  be  found  a  little  north  and  east  of  a  Cygni, 
and  between  the  extremes  of  abundance  and  poverty  here 
noted  there  may  be  found  every  gradation  of  nebulous 
light. 

The  Milky  Way  is  not  so  simple  in  its  structure  as  might 
at  first  be  thought,  but  a  clear  and  moonless  night  is 
required  to  bring  out  its  details.  The  nature  of  these 
details,  the  structure  of  the  galaxy,  its  shape  and  extent, 
the  arrangement  of  its  parts,  and  their  relation  to  stars 
and  nebulae  in  general,  have  been  subjects  of  much  specu- 
lation by  astronomers  and  others  who  have  sought  to  trace 
out  in  this  way  what  is  called  the  construction  of  the 
heavens. 

220.  Distribution  of  the  stars. — How  far  out  into  space 
do  the  stars  extend  ?  Are  they  limited  or  infinite  in  num- 
ber ?  Do  they  form  a  system  of  mutually  related  parts,  or 
are  they  bunched  promiscuously,  each  for  itself,  without 
reference  to  the  others  ?  Here  is  what  has  been  well  called 
"the  most  important  problem  of  stellar  astronomy,  the 
acquisition  of  well-founded  ideas  about  the  distribution  of 
the  stars."  While  many  of  the  ideas  upon  this  subject 
which  have  been  advanced  by  eminent  astronomers  and 
which  are  still  current  in  the  books  are  certainly  wrong, 
and  few  of  their  speculations  along  this  line  are  demon- 
strably  true,  the  theme  itself  is  of  such  grandeur  and  per- 
manent interest  as  to  demand  at  least  a  brief  considera- 
tion. But  before  proceeding  to  its  speculative  side  we 
need  to  collect  facts  upon  which  to  build,  and  these,  how- 
ever inadequate,  are  in  the  main  simple  and  not  far  to  seek. 

Parallaxes,  proper  motions,  motions  in  the  line  of  sight, 
while  pertinent  to  the  problem  of  stellar  distribution,  are 


352  ASTRONOMY 

of  small  avail,  since  they  are  far  too  scanty  in  number  and 
relate  only  to  limited  classes  of  stars,  usually  the  very 
bright  ones  or  those  nearest  to  the  sun.  Almost  the  sole 
available  data  are  contained  in  the  brightness  of  the  stars 
and  the  way  in  which  they  seem  scattered  in  the  sky.  The 
most  casual  survey  of  the  heavens  is  enough  to  show  that 
the  stars  are  not  evenly  sprinkled  upon  it.  The  lucid  stars 
are  abundant  in  some  regions,  few  in  others,  and  the  labori- 
ous star  gauges,  actual  counting  of  the  stars  in  sample 
regions  of  the  sky,  which  have  been  made  by  the  Herschels, 
Celoria,  and  others,  suffice  to  show  that  this  lack  of  uni- 
formity in  distribution  is  even  more  markedly  true  of  the 
telescopic  stars. 

The  rate  of  increase  in  the  number  of  stars  from  one 
magnitude  to  the  next,  as  shown  in  §  187,  is  proof  of 
another  kind  of  irregularity  in  their  distribution.  It  is  not 
difficult  to  show,  mathematically,  that  if  in  distant  regions 
of  space  the  stars  were  on  the  average  as  numerous  and  as 
bright  as  they  are  in  the  regions  nearer  to  the  sun,  then 
the  stars  of  any  particular  magnitude  ought  to  be  four 
times  as  numerous  as  those  of  the  next  brighter  magnitude 
— e.  g.,  four  times  as  many  sixth-magnitude  stars  as  there 
are  fifth-magnitude  ones.  But,  as  we  have  already  seen  in 
§  187,  by  actual  count  there  are  only  three  times  as  many, 
and  from  the  discrepancy  between  these  numbers,  an  actual 
threefold  increase  instead  of  a  fourfold  one,  we  must  con- 
clude that  on  the  whole  the  stars  near  the  sun  are  either 
bigger  or  brighter  or  more  numerous  than  in  the  remoter 
depths  of  space. 

221.  The  stellar  system, — But  the  arrangement  of  the 
stars  is  not  altogether  lawless  and  chaotic  ;  there  are  traces 
of  order  and  system,  and  among  these  the  Milky  Way  is  the 
dominant  feature.  Telescope  and  photographic  plate  alike 
show  that  it  is  made  up  of  stars  which,  although  quite  ir- 
regularly scattered  along  its  course,  are  on  the  average 
some  twenty  times  as  numerous  in  the  galaxy  as  at  its 


STARS  AND  NEBULAE  353 

poles,  and  which  thin  out  as  we  recede  from  it  on  either 
side,  at  first  rapidly  and  then  more  slowly.  This  tendency 
to  cluster  along  the  Milky  Way  is  much  more  pronounced 
among  the  very  faint  telescopic  stars  than  among  the 
brighter  ones,  for  the  lucid  stars  and  the  telescopic  ones 
down  to  the  tenth  or  eleventh  magnitude,  while  very 
plainly  showing  the  clustering  tendency,  are  not  more  than 
three  times  as  numerous  in  the  galaxy  as  in  the  constella- 
tions most  remote  from  it.  It  is  remarkable  as  showing 
the  condensation  of  the  brightest  stars  that  one  half  of  all 
the  stars  in  the  sky  which  are  brighter  than  the  second 
magnitude  are  included  within  a  belt  extending  12°  on 
either  side  of  the  center  line  of  the  galaxy. 

In  addition  to  this  general  condensation  of  stars  toward 
the  Milky  Way,  there  are  peculiarities  in  the  distribution  of 
certain  classes  of  stars  which  are  worth  attention.  Planet- 
ary nebulae  and  new  stars  are  seldom,  if  ever,  found  far 
from  the  Milky  Way,  and  stars  with  bright  lines  in  their 
spectra  especially  affect  this  region  of  the  sky.  Stars  with 
spectra  of  the  first  type — Sirian  stars — are  much  more 
strongly  condensed  toward  the  Milky  Way  than  are  stars 
of  the  solar  type,  and  in  consequence  of  this  the  Milky 
Way  is  peculiarly  rich  in  light  of  short  wave  lengths.  Ee- 
solvable  star  clusters  are  so  much  more  numerous  in  the 
galaxy  than  elsewhere,  that  its  course  across  the  sky  would 
be  plainly  indicated  by  their  grouping  upon  a  map  showing 
nothing  but  clusters  of  this  kind. 

On  the  other  hand,  nebulae  as  a  class  show  a  distinct 
aversion  for  the  galaxy,  and  are  found  most  abundantly  in 
those  parts  of  the  sky  farthest  from  it,  much  as  if  they 
represented  raw  material  which  was  lacking  along  the 
Milky  Way,  because  already  worked  up  to  make  the  stars 
which  are  there  so  numerous. 

222.  Relation  of  the  sun  to  the  Milky  Way.— The  fact 
that  the  galaxy  is  a  great  circle  of  the  sky,  but  only  of  mod- 
erate width,  shows  that  it  is  a  widely  extended  and  com- 


354  ASTRONOMY 

paratively  thin  stratum  of  stars  within  which  the  solar  sys- 
tem lies,  a  member  of  the  galactic  system,  and  probably  not 
very  far  from  its  center.  This  position,  however,  is  not  to 
be  looked  upon  as  a  permanent  one,  since  the  sun's  motion, 
which  lies  nearly  in  the  plane  of  the  Milky  Way,  is  cease- 
lessly altering  its  relation  to  the  center  of  that  system,  and 
may  ultimately  carry  us  outside  its  limits. 

The  Milky  Way  itself  is  commonly  thought  to  be  a 
ring,  or  series  of  rings,  like  the  coils  of  the  great  spiral 
nebula  in  Andromeda,  and  separated  from  us  by  a  space  far 
greater  than  the  thickness  of  the  ring  itself.  Note  in  Figs. 
149  and  150  how  the  background  is  made  up  of  bright  and 
dark  parts  curiously  interlaced,  and  presenting  much  the 
appearance  of  a  thin  sheet  of  cloud  through  which  we  look 
to  barren  space  beyond.  While,  mathematically,  this  ap- 
pearance can  not  be  considered  as  proof  that  the  galaxy 
is  in  fact  a  distant  ring,  rather  than  a  sheet  of  starry 
matter  stretching  continuously  from  the  nearer  stellar 
neighbors  of  the  sun  into  the  remotest  depths  of  space, 
nevertheless,  most  students  of  the  question  hold  it  to  be 
such  a  ring  of  stars,  which  are  relatively  close  together 
while  its  center  is  comparativeljjyag^i.  although  even 
here  are  1^01116  liuiiTIreds'ol1  Ln'ousanos  of  stars  which  on  the 
whole  have  a  tendency  to  cluster  near  its  plane  and  to 
crowd  together  a  little  more  densely  than  elsewhere  in  the 
region  where  the  sun  is  placed. 

223.  Dimensions  of  the  galaxy, — The  dimensions  of  this 
stellar  system  are  wholly  unknown,  but  there  can  be  no 
doubt  that  it  extends  farther  in  the  plane  of  the  Milky 
Way  than  at  right  angles  to  that  plane,  for  stars  of  the  fif- 
teenth and  sixteenth  magnitudes  are  common  in  the  galaxy, 
and  testify  by  their  feeble  light  to  their  great  distance 
from  the  earth,  while  near  the  poles  of  the  Milky  Way  there 
seem  to  be  few  stars  fainter  than  the  twelfth  magnitude. 
Herschel,  with  his  telescope  of  18  inches  aperture,  could 
count  in  the  Milky  Way  more  than  a  dozen  times  as  many 


STARS  AND  NEBULA  355 

stars  per  square  degree  as  could  Celoria  with  a  telescope  of 
4  inches  aperture ;  but  around  the  poles  of  the  galaxy  the 
two  telescopes  showed  practically  the  same  number  of  stars, 
indicating  that  here  even  the  smaller  telescope  reached  to 
the  limits  of  the  stellar  system.  Very  recently,  indeed,  the . 
telescope  with  which  Fig.  140  was  photographed  seems  to 
have  reached  the  farthest  limit  of  the  Milky  Way,  for  on  a 
photographic  plate  of  one  of  its  richest  regions  Roberts 
finds  it  completely  resolved  into  stars  which  stand  out  upon 
a  black  background  with  no  trace  of  nebulous  light  between 
them. 

224,.  Beyond  the  Milky  Way.— Each  additional  step  into 
the  depths  of  space  brings  us  into  a  region  of  which  less  is 
known,  and  what  lies  beyond  the  Milky  Way  is  largely  a 
matter  of  conjecture.  We  shrink  from  thinking  it  an  in- 
finite void,  endless  emptiness,  and  our  intellectual  sympa- 
thies go  out  to  Lambert's  speculation  of  a  universe  filled 
with  stellar  systems,  of  which  ours,  bounded  by  the  galaxy, 
is  only  one.  There  is,  indeed,  little  direct  evidence  that 
other  such  systems  exist,  but  the  Andromeda  nebula  is  not 
altogether  unlike  a  galaxy  with  a  central  cloud  of  stars, 
and  in  the  southern  hemisphere,  invisible  in  our  latitudes, 
are  two  remarkable  stellar  bodies  like  the  Milky  Way  in 
appearance,  but  cut  off  from  all  apparent  connection  with 
it,  much  as  we  might  expect  to  find  independent  stellar 
systems,  if  such  there  be. 

These  two  bodies  are  known  as  the  Magellanic  clouds, 
and  individually  bear  the  names  of  Major  and  Minor  Xubec- 
ula.  According  to  Sir  John  Herschel,  "  the  Xubecula 
Major,  like  the  Minor,  consists  partly  of  large  tracts  and 
ill-defined  patches  of  irresolvable  nebula,  and  of  nebulosity 
in  every  stage  of  resolution  up  to  perfectly  resolved  stars 
like  the  Milky  Way,  as  also  of  regular  and  irregular  nebulae 
...  of  globular  clusters  in  every  stage  of  resolvability,  and 
of  clustering  groups  sufficiently  insulated  and  condensed  to 
come  under  the  designation  of  clusters  of  stars."  Its  out- 


356  ASTRONOMY 

lines  are  vague  and  somewhat  uncertain,  but  surely  include 
an  area  of  more  than  40  square  degrees — i.  e.,  as  much  as 
the  bowl  of  the  Big  Dipper — and  within  this  area  Herschel 
counted  several  hundred  nebulse  and  clusters  "  which  far 
exceeds  anything  that  is  to  be  met  with  in  any  other  region 
of  the  heavens."  Although  its  excessive  complexity  of  de- 
tail baffled  Herschel's  attempts  at  artistic  delineation,  it 
has  yielded  to  the  modern  photographic  processes,  which 
show  the  Nubecula  Major  to  be  an  enormous  spiral  nebula 
made  up  of  subordinate  stars,  nebula?,  and  clusters,  as  is 
the  Milky  Way. 

Compared  with  the  Andromeda  nebula,  its  greater  angu- 
lar extent  suggests  a  smaller  distance,  although  for  the 
present  all  efforts  at  determining  the  parallax  of  either 
seem  hopeless.  But  the  spiral  form  which  is  common  to 
both  suggests  that  the  Milky  Way  itself  may  be  a  gigantic 
spiral  nebula  near  whose  center  lies  the  sun,  a  humble 
member  of  a  great  cluster  of  stars  which  is  roughly  globu- 
lar in  shape,  but  flattened  at  the  poles  of  the  galaxy 
and  completely  encircled  by  its  coils.  However  plausible 
such  a  view  may  appear,  it  is  for  the  present,  at  least,  pure 
hypothesis,  although  vigorously  advocated  by  Easton,  who 
bases  his  argument  upon  the  appearance  of  the  galaxy 
itself. 

225.  Absorption  of  starlight. — We  have  had  abundant 
occasion  to  learn  that  at  least  within  the  confines  of  the 
solar  system  meteoric  matter,  cosmic  dust,  is  profusely  scat- 
tered, and  it  appears  not  improbable  that  the  same  is  true, 
although  in  smaller  degree,  in  even  the  remoter  parts  of 
space.  In  this  case  the  light  which  comes  from  the  farther 
stars  over  a  path  requiring  many  centuries  to  travel,  must 
be  in  some  measure  absorbed  and  enfeebled  by  the  obstacles 
which  it  encounters  on  the  way.  Unless  celestial  space  is 
transparent  to  an  improbable  degree  the  remoter  stars  do 
not  show  their  true  brightness ;  there  is  a  certain  limit 
beyond  which  no  star  is  able  to  send  its  light,  and  beyond 


STARS  AND  NEBULA  357 

which  the  universe  must  be  to  us  a  blank.  A  lighthouse 
throws  into  the  fog  its  beams  only  to  have  them  extin- 
guished before  a  single  mile  is  passed,  and  though  the 
celestial  lights  shine  farther,  a  limit  to  their  reach  is  none 
the  less  certain  if  meteoric  dust  exists  outside  the  solar 
system.  If  there  is  such  an  absorption  of  light  in  space, 
as  seems  plausible,  the  universe  may  well  be  limitless  and 
the  number  of  stellar  systems  infinite,  although  the  most 
attenuated  of  dust  clouds  suffices  to  conceal  from  us  and 
to  shut  off  from  our  investigation  all  save  a  minor  fraction 
of  it  and  them. 


CHAPTEE   XV 

GROWTH   AND   DECAY 

226.  Nature  of  the  problem. — To  use  a  common  figure  of 
speech,  the  universe  is  alive.  We  have  found  it  filled  with 
an  activity  that  manifests  itself  not  only  in  the  motions  of 
the  heavenly  bodies  along  their  orbits,  but  which  extends 
to  their  minutest  parts,  the  molecules  and  atoms,  whose 
vibrations  furnish  the  radiant  energy  given  off  by  sun  and 
stars.  Some  of  these  activities,  such  as  the  motions  of  the 
heavenly  bodies  in  their  orbits,  seem  fitted  to  be  of  endless 
duration ;  while  others,  like  the  radiation  of  light  and  heat, 
are  surely  temporary,  and  sooner  or  later  must  come  to  an 
end  and  be  replaced  by  something  different.  The  study  of 
things  as  they  are  thus  leads  inevitably  to  questions  of 
what  has  been  and  what  is  to  be.  A  sound  science  should 
furnish  some  account  of  the  universe  of  yesterday  and 
to-morrow  as  well  as  of  to-day,  and  we  need  not  shrink 
from  such  questions,  although  answers  to  them  must  be 
vague  and  in  great  measure  speculative. 

The  historian  of  America  finds  little  difficulty  with  events 
of  the  nineteenth  century  or  even  the  eighteenth,  but  the 
sources  of  information  about  America  in  the  fifteenth  cen- 
tury are  much  less  definite  ;  the  tenth  century  presents 
almost  a  blank,  and  the  history  of  American  mankind  in 
the  first  century  of  the  Christian  era  is  wholly  unknown. 
So,  as  we  attempt  to  look  into  the  past  or  the  future  of  the 
heavens,  we  must  expect  to  find  the  mists  of  obscurity  grow 
denser  with  remoter  periods  until  even  the  vaguest  outlines 
of  its  development  are  lost,  and  we  are  compelled  to  say, 
358 


GROWTH  AND   DECAY  359 

beyond  this  lies  the  unknown.  Our  account  of  growth  and 
decay  in  the  universe,  therefore,  can  not  aspire  to  cover  the 
whole  duration  of  things,  but  must  be  limited  in  its  scope 
to  certain  chapters  whose  epochs  lie  near  to  the  time  in 
which  we  live,  and  even  for  these  we  need  to  bear  con- 
stantly in  mind  the  logical  bases  of  such  an  inquiry  and 
the  limitations  which  they  impose  upon  us. 

227.  Logical  bases  and  limitations. — The  first  of  these 
bases  is :  An  adequate  knowledge  of  the  present  universe. 
Our  only  hope  of  reading  the  past  and  future  lies  in  an 
understanding  of  the  present;  not  necessarily  a  complete 
knowledge  of  it,  but  one  which  is  sound  so  far  as  it  goes. 
Our  position  is  like  that  of  a  detective  who  is  called  upon 
to  unravel  a  mystery  or  crime,  and  who  must  commence 
with  the  traces  that  have  been  left  behind  in  its  commis- 
sion. The  foot  print,  the  blood  stain,  the  broken  glass  must 
be  examined  and  compared,  and  fashioned  into  a  theory  of 
how  they  came  to  be  ;  and  as  a  wrong  understanding  of 
these  elements  is  sure  to  vitiate  the  theories  based  upon 
them,  so  a  false  science  of  the  universe  as  it  now  is,  will 
surely  give  a  false  account  of  what  it  has  been;  while  a 
correct  but  incomplete  knowledge  of  the  present  does  not 
wholly  bar  an  understanding  of  the  past,  but  only  puts  us 
in  the  position  of  the  detective  who  correctly  understands 
what  he  sees  but  fails  to  take  note  of  other  facts  which 
might  greatly  aid  him. 

The  second  basis  of  our  inquiry  is :  The  assumed  per- 
manence of  natural  laws.  The  law  of  gravitation  certainly 
held  true  a  century  ago  as  well  as  a  year  ago,  and  for  aught 
we  know  to  the  contrary  it  may  have  been  a  law  of  the  uni- 
verse for  untold  millions  of  years ;  but  that  it  has  prevailed 
for  so  long  a  time  is  a  pure  assumption,  although  a  neces- 
sary one  for  our  purpose.  So  with  those  other  laws  of 
mathematics  and  mechanics  and  physics  and  chemistry  to 
which  we  must  appeal ;  if  there  was  ever  a  time  or  place 
in  which  they  did  not  hold  true,  that  time  and  place  lie 


360  ASTRONOMY 

beyond  the  scope  of  our  inquiry,  and  are  in  the  domain 
inaccessible  to  scientific  research.  It  is  for  this  reason 
that  science  knows  nothing  and  can  know  nothing  of  a 
creation  or  an  end  of  the  universe,  but  considers  only  its 
orderly  development  within  limited  periods  of  time.  What 
kind  of  a  past  universe  would,  under  the  operation  of 
known  laws,  develop  into  the  present  one,  is  the  question 
with  which  we  have  to  deal,  and  of  it  we  may  say  with 
Helmholtz  :  "  From  the  standpoint  of  science  this  is  no 
idle  speculation  but  an  inquiry  concerning  the  limitations 
of  its  methods  and  the  scope  of  its  known  laws." 

To  ferret  out  the  processes  by  which  the  heavenly  bodies 
have  been  brought  to  their  present  condition  we  seek  first 
of  all  for  lines  of  development  now  in  progress  which  tend 
to  change  the  existing  order  of  things  into  something  dif- 
ferent, and,  having  found  these,  to  trace  their  effects  into 
both  past  and  future.  Any  force,  however  small,  or  any 
process,  however  slow,  may  produce  great  results  if  it  works 
always  and  ceaselessly  in  the  same  direction,  and  it  is  in 
these  processes,  whose  trend  is  never  reversed,  that  we  find 
a  partial  clew  to  both  past  and  future. 

228.  The  sun's  development.— The  first  of  these  to  claim 
our  attention  is  the  shrinking  of  the  sun's  diameter  which, 
as  we  have  seen  in  Chapter  X,  is  the  means  by  which  the 
solar  output  of  radiant  energy  is  maintained  from  year  to 
year.  Its  amount,  only  a  few  feet  per  annum,  is  far  too 
small  to  be  measured  with  any  telescope  ;  but  it  is  cumula- 
tive, working  century  after  century  in  the  same  direction, 
and,  given  time  enough,  it  will  produce  in  the  future,  and 
must  have  produced  in  the  past,  enormous  transformations 
in  the  sun's  bulk  and  equally  significant  changes  in  its 
physical  condition. 

Thus,  as  we  attempt  to  trace  the  sun's  history  into  the 
past,  the  farther  back  we  go  the  greater  shall  we  expect  to 
find  its  diameter  and  the  greater  the  space  (volume) 
through  which  its  molecules  are  spread.  By  reason  of  this 


GROWTH  AND  DECAY  361 

expansion  its  density  must  have  been  less  then  than  now, 
and  by  going  far  enough  back  we  may  even  reach  a  time  at 
which  the  density  was  comparable  with  what  we  find  in  the 
nebulae  of  to-day.  If  our  ideas  of  the  sun's  present  mechan- 
ism are  sound,  then,  as  a  necessary  consequence  of  these,, 
its  past  career  must  have  been  a  process  of  condensation  in 
which  its  component  particles  were  year  by  year  packed 
closer  together  by  their  own  attraction  for  each  other.  As 
we  have  seen  in  §  126,  this  condensation  necessarily  devel- 
oped heat,  a  part  of  which  was  radiated  away  as  fast  as  pro- 
duced, while  the  remainder  was  stored  up,  and  served  to 
raise  the  temperature  of  the  sun  to  what  we  find  it  now. 
At  the  present  time  this  temperature  is  a  chief  obstacle  to 
further  shrinkage,  and  so  powerfully  opposes  the  gravita- 
tive  forces  as  to  maintain  nearly  an  equilibrium  with  them, 
thus  causing  a  very  slow  rate  of  further  condensation.  But 
it  is  not  probable  that  this  was  always  so.  In  the  early 
stages  of  the  sun's  history,  when  the  temperature  was  low, 
contraction  of  its  bulk  must  have  been  more  rapid,  and 
attempts  have  been  made  by  the  mathematicians  to  measure 
its  rate  of  progress  and  to  determine  how  long  a  time  has 
been  consumed  in  the  development  of  the  present  sun  from 
a  primitive  nebulous  condition  in  which  it  filled  a  space  of 
greater  diameter  than  Xeptune's  orbit.  Of  course,  numer- 
ical precision  is  not  to  be  expected  in  results  of  this  kind, 
but,  from  a  consideration  of  the  greatest  amount  of  heat 
that  could  be  furnished  by  the  shrinkage  of  a  mass  equal  to 
that  of  the  sun,  it  seems  that  the  period  of  this  develop- 
ment is  to  be  measured  in  tens  of  millions  or  possibly  hun- 
dreds of  millions  of  years,  but  almost  certainly  does  not 
reach  a  thousand  millions. 

229.  The  sun's  future,— The  future  duration  of  the  sun 
as  a  source  of  radiant  energy  is  surely  to  be  measured  in 
far  smaller  numbers  than  these.  Its  career  as  a  dispenser 
of  light  and  heat  is  much  more  than  half  spent,  for  the 
shrinkage  results  in  an  ever-increasing  density,  which 
24 


362  ASTRONOMY 

makes  its  gaseous  substance  approximate  more  and  more 
toward  the  behavior  of  a  liquid  or  solid,  and  we  recall  that 
these  forms  of  matter  can  not  by  any  further  condensation 
restore  the  heat  whose  loss  through  radiation  caused  them 
to  contract.  They  may  continue  to  shrink,  but  their  tem- 
perature must  fall,  and  when  the  sun's  substance  becomes 
too  dense  to  obey  the  laws  of  gaseous  matter  its  surface 
must  cool  rapidly  as  a  consequence  of  the  radiation  into 
surrounding  space,  and  must  congeal  into  a  crust  which, 
although  at  first  incandescent,  will  speedily  become  dark 
and  opaque,  cutting  off  the  light  of  the  central  portions, 
save  as  it  may  be  rent  from  time  to  time  by  volcanic 
outbursts  of  the  still  incandescent  mass  beneath.  But 
such  outbursts  can  be  of  short  duration  only,  and  its  final 
.condition  must  be  that  of  a  dark  body,  like  the  earth  or 
moon,  no  longer  available  as  a  source  of  radiant  energy. 
Even  before  the  formation  of  a  solid  crust  it  is  quite  pos- 
sible that  the  output  of  light  and  heat  may  be  seriously 
diminished  by  the  formation  of  dense  vapors  completely 
enshrouding  it,  as  is  now  the  case  with  Jupiter  and  Saturn. 
It  is  believed  that  these  planets  were  formerly  incandescent, 
and  at  the  present  time  are  in  a  state  of  development 
through  which  the  earth  has  passed  and  toward  which  the 
sun  is  moving.  According  to  Kewcomb,  the  future  during 
which  the  sun  can  continue  to  furnish  light  and  heat  at  its 
present  rate  is  not  likely  to  exceed  10,000,000  years. 

This  idea  of  the  sun  as  a  developing  body  whose  pres- 
ent state  is  only  temporary,  furnishes  a  clew  to  some  of  the 
vexing  problems  of  solar  physics.  Thus  the  sun-spot  period, 
the  distribution  of  the  spots  in  latitude,  and  the  peculiar 
law  of  rotation  of  the  sun  in  different  latitudes,  may  be, 
and  very  probably  are,  results  not  of  anything  now  operat- 
ing beneath  its  photosphere,  but  of  something  which  hap- 
pened to  it  in  the  remote  past — e.  g.,  an  unsymmetrical 
shrinkage  or  possibly  a  collision  with  some  other  body.  At 
sea  the  waves  continue  to  toss  long  after  the  storm  which 


GROWTH  AND  DECAY  363 

produced  them  has  disappeared,  and,  according  to  the 
mathematical  researches  of  Wilsing,  a  profound  agitation 
of  the  sun's  mass  might  well  require  tens  of  thousands,  or 
even  hundreds  of  thousands  of  years  to  subside,  and  during 
this  time  its  effects  would  be  visible,  like  the  waves,  as  phe- 
nomena  for  which  the  actual  condition  of  things  furnishes 
no  apparent  cause. 

230.  The  nebular  hypothesis. — The  theory  of  the  sun's 
progressive  contraction  as  a  necessary  result  of  its  radiation 
of  energy  is  comparatively  modern,  but  more  than  a  cen- 
tury ago  philosophic  students  of  Nature  had  been  led  in 
quite  a  different  way  to  the  belief  that  in  the  earlier  stages 
of  its  career  the  sun  must  have  been  an  enormously  ex- 
tended body  whose  outer  portions  reached  even  beyond  the 
orbit  of  the  remotest  planet.  Laplace,  whose  speculations 
upon  this  subject  have  had  a  dominant  influence  during 
the  nineteenth  century,  has  left,  in  a  popular  treatise  upon 
astronomy,  an  admirable  statement  of  the  phenomena  of 
planetary  motion,  which  suggest  and  lead  up  to  the  nebular 
theory  of  the  sun's  development,  and  in  presenting  this 
theory  we  shall  follow  substantially  his  line  of  thought, 
but  with  some  freedom  of  translation  and  many  omissions. 

He  says  :  "  To  trace  out  the  primitive  source  of  the  plan- 
etary movements,  we  have  the  following  five  phenomena : 
(1)  These  movements  all  take  place  in  the  same  direction 
and  nearly  in  the  same  plane.  (2)  The  movements  of  the 
satellites  are  in  the  same  direction  as  those  of  the  planets. 
(3)  The  rotations  of  the  planets  and  the  sun  are  in  the 
same  direction  as  the  orbital  motions  and  nearly  in  the  same 
plane.  (4)  Planets  and  satellites  alike  have  nearly  circular 
orbits.  (5)  The  orbits  of  comets  are  wholly  unlike  these  by 
reason  of  their  great  eccentricities  and  inclinations  to  the 
ecliptic."  That  these  coincidences  should  be  purely  the 
result  of  chance  seemed  to  Laplace  incredible,  and,  seeking 
a  cause  for  them,  he  continues  :  "  Whatever  its  nature  may 
be,  since  it  has  produced  or  controlled  the  motions  of  the 


364  ASTRONOMY 

planets,  it  must  have  reached  out  to  all  these  bodies,  and,  in 
view  of  the  prodigious  distances  which  separate  them,  the 
cause  can  have  been  nothing  else  than  a  fluid  of  great  ex- 
tent which  must  have  enveloped  the  sun  like  an  atmosphere. 
A  consideration  of  the  planetary  motions  leads  us  to  think 
that  .  .  .  the  sun's  atmosphere  formerly  extended  far  be- 
yond the  orbits  of  all  the  planets  and  has  shrunk  by  degrees 
to  its  present  dimensions."  This  is  not  very  different  from 
the  idea  developed  in  §  228  from  a  consideration  of  the 
sun's  radiant  energy ;  but  in  Laplace's  day  the  possibility 
of  generating  the  sun's  heat  by  contraction  of  its  bulk  was 
unknown,  and  he  was  compelled  to  assume  a  very  high  tem- 
perature for  the  primitive  nebulous  sun,  while  we  now  know 
that  this  is  unnecessary.  Whether  the  primitive  nebula 
was  hot  or  cold  the  shrinkage  would  take  place  in  much 
the  same  way,  and  would  finally  result  in  a  star  or  sun  of 
very  high  temperature,  but  its  development  would  be  slower 
if  it  were  hot  in  the  beginning  than  if  it  were  cold. 

But  again  Laplace :  "  How  did  the  sun's  atmosphere 
determine  the  rotations  and  revolutions  of  planets  and 
satellites  ?  If  these  bodies  had  been  deeply  immersed  in 
this  atmosphere  its  resistance  to  their  motion  would  have 
made  them  fall  into  the  sun,  and  we  may  therefore  conjec- 
ture that  the  planets  were  formed,  one  by  one,  at  the  outer 
limits  of  the  solar  atmosphere  by  the  condensation  of  zones 
of  vapor  which  were  cast  off  in  the  plane  of  the  sun's  equa- 
tor." Here  he  proceeds  to  show  by  an  appeal  to  dynamical 
principles  that  something  of  this  kind  must  happen,  and 
that  the  matter  sloughed  off  by  the  nebula  in  the  form  of  a 
ring,  perhaps  comparable  to  the  rings  of  Saturn  or  the 
asteroid  zone,  would  ultimately  condense  into  a  planet, 
which  in  its  turn  might  shrink  and  cast  off  rings  to  pro- 
duce satellites. 

Planets  and  satellites  would  then  all  have  similar  mo- 
tions, as  noted  at  the  beginning  of  this  section,  since  in 
every  case  this  motion  is  an  inheritance  from  a  common 


PIERRE  SIMON  LAPLACE   (1749-1827). 


GROWTH  AND  DECAY  365 

source,  the  rotation  of  the  primitive  nebula  about  its  own 
axis.  "  All  the  bodies  which  circle  around  a  planet  having 
been  thus  formed  from  rings  which  its  atmosphere  succes- 
sively abandoned  as  rotation  became  more  and  more  rapid, 
this  rotation  should  take  place  in  less  time  than  is  required 
for  the  orbital  revolution  of  any  of  the  bodies  which  have 
been  cast  off,  and  this  holds  true  for  the  sun  as  compared 
with  the  planets." 

231.  Objections  to  the  nebular  hypothesis. — In  Laplace's 
time  this  slower  rate  of  motion  was  also  supposed  to  hold 
true  for  Saturn's  rings  as  compared  with  the  rotation  of 
Saturn  itself,  but,  as  we  have  seen  in  Chapter  XI,  this  ring  is 
made  up  of  a  great  number  of  independent  particles  which 
move  at  different  rates  of  speed,  and  comparing,  through 
Kepler's  Third  Law,  the  motion  of  the  inner  edge  of  the 
ring  with  the  known  periodic  time  of  the  satellites,  we  may 
find  that  these  particles  must  rotate  about  Saturn  more 
rapidly  than  the  planet  turns  upon  its  axis.  Similarly  the 
inner  satellite  of  Mars  completes  its  revolution  in  about 
one  third  of  a  Martian  day,  and  we  find  in  cases  like  this 
grounds  for  objection  to  the  nebular  theory.  Compare  also 
Laplace's  argument  with  the  peculiar  rotations  of  Uranus, 
Neptune;  and  their  satellites  (Chapter  XI).  Do  these  for- 
tify or  weaken  his  case  ? 

Despite  these  objections  and  others  equally  serious  that 
have  been  raised,  the  nebular  theory  agrees  with  the  facts 
of  Nature  at  so  many  points  that  astronomers  upon  the 
whole  are  strongly  inclined  to  accept  its  major  outlines  as 
being  at  least  an  approximation  to  the  course  of  develop- 
ment actually  followed  by  the  solar  system ;  but  at  some 
points — e.  g.,  the  formation  of  planets  and  satellites  through 
the  casting  off  of  nebulous  rings — the  objections  are  so 
many  and  strong  as  to  call  for  revision  and  possibly  serious 
modification  of  the  theory. 

One  proposed  modification,  much  discussed  in  recent 
years,  consists  in  substituting  for  the  primitive  gaseous 


366  ASTRONOMY 

nebula  imagined  by  Laplace,  a  very  diffuse  cloud  of  mete- 
oric matter  which  in  the  course  of  its  development  would 
become  transformed  into  the  gaseous  state  by  rising  tem- 
perature. From  this  point  of  view  much  of  the  meteoric 
dust  still  scattered  throughout  the  solar  system  may  be 
only  the  fragments  left  over  in  fashioning  the  sun  and 
planets.  Chamberlin  and  Moulton,  who  have  recently 
given  much  attention  to  this  subject,  in  dissenting  from 
some  of  Laplace's  views,  consider  that  the  primitive  nebu- 
lous condition  must  have  been  one  in  which  the  matter  of 
the  system  was  "  so  brought  together  as  to  give  low  mass, 
high  momentum,  and  irregular  distribution  to  the  outer 
part,  and  high  mass,  low  momentum,  and  sphericity  to  the 
central  part,"  and  they  suggest  a  possible  oblique  collision 
of  a  small  nebula  with  the  outer  parts  of  a  large  one. 

232.  Bode's  law. — We  should  not  leave  the  theory  of 
Laplace  without  noting  the  light  it  casts  upon  one  point 
otherwise  obscure — the  meaning  of  Bode's  law  (§  134). 
This  law,  stated  in  mathematical  form,  makes  a  geomet- 
rical series,  and  similar  geometrical  series  apply  to  the 
distances  of  the  satellites  of  Jupiter  and  Saturn  from 
these  planets.  Now,  Eoche  has  shown  by  the  application 
of  physical  laws  to  the  shrinkage  of  a  gaseous  body  that 
its  radius  at  any  time  may  be  expressed  by  means  of  a 
certain  mathematical  formula  very  similar  to  Bode's  law, 
save  that  it  involves  the  amount  of  time  that  has  elapsed 
since  the  beginning  of  the  shrinking  process.  By  compar- 
ing this  formula  with  the  one  corresponding  to  Bode's  law 
he  reaches  the  conclusion  that  the  peculiar  spacing  of  the 
planets  expressed  by  that  law  means  that  they  were  formed 
at  successive  equal  intervals  of  time — i.  e.,  that  Mars  is  as 
much  older  than  the  earth  as  the  earth  is  older  than 
Venus,  etc.  The  failure  of  Bode's  law  in  the  case  of 
Neptune  would  then  imply  that  the  interval  of  time  be- 
tween the  formation  of  Neptune  and  Uranus  was  shorter 
than  that  which  has  prevailed  for  the  other  planets.  But 


GROWTH  AND  DECAY  367 

too  much  stress  should  not  be  placed  upon  this  conclusion. 
So  long  as  the  manner  in  which  the  planets  came  into  being 
continues  an  open  question,  conclusions  about  their  time 
of  birth  must  remain  of  doubtful  validity. 

233.  Tidal  friction  between  earth  and  moon. — An  impor- 
tant addition  to  theories  of  development  within  the  solar 
system  has  been  worked  out  by  Prof.  G.  H.  Darwin,  who, 
starting  with  certain  very  simple  assumptions  as  to  the 
present  condition  of  things  in  earth  and  moon,  derives 
from  these,  by  a  strict  process  of  mathematical  reasoning, 
far-reaching  conclusions  of  great  interest  and  importance. 
The  key  to  these  conclusions  lies  in  recognition  of  the  fact 
that  through  the  influence  of  the  tides  (§  42)  there  is  now 
in  progress  and  has  been  in  progress  for  a  very  long  time,  a 
gradual  transfer  of  motion  (moment  of  momentum)  from 
the  earth  to  the  moon.  The  earth's  motion  of  rotation  is 
being  slowly  destroyed  by  the  friction  of  the  tides,  as  the 
motion  of  a  bicycle  is  destroyed  by  the  friction  of  a  brake, 
and,  in  consequence  of  this  slowing  down,  the  moon  is 
pushed  farther  and  farther  away  from  the  earth,  so  that 
it  now  moves  in  a  larger  orbit  than  it  had  some  millions 
of  years  ago. 

Fig.  24  has  been  used  to  illustrate  the  action  of  the 
moon  in  raising  tides  upon  the  earth,  but  in  accordance 
with  the  third  law  of  motion  (§  36)  this  action  must  be 
accompanied  by  an  equal  and  contrary  reaction  whose 
nature  may  readily  be  seen  from  the  same  figure.  The 
moon  moves  about  its  orbit  from  west  to  east  and  the 
earth  rotates  about  its  axis  in  the  same  direction,  as 
shown  by  the  curved  arrow  in  the  figure.  The  tidal  wave, 
/,  therefore  points  a  little  in  advance  of  the  moon's  posi- 
tion in  its  orbit  and  by  its  attraction  must  tend  to  pull  the 
moon  ahead  in  its  orbital  motion  a  little  faster  than  it 
would  move  if  the  whole  substance  of  the  earth  were 
placed  inside  the  sphere  represented  by  the  broken  circle 
in  the  figure.  It  is  true  that  the  tidal  wave  at  I"  pulls 


368  ASTRONOMY 

back  and  tends  to  neutralize  the  effect  of  the  wave  at  /, 
but  on  the  whole  the  tidal  wave  nearer  the  moon  has  the 
stronger  influence,  and  the  moon  on  the  whole  moves  a 
very  little  faster,  and  by  virtue  of  this  added  impetus 
draws  continually  a  little  farther  away  from  the  earth 
than  it  would  if  there  were  no  tides. 

234.  Consequences  of  tidal  friction  upon  the  earth. — This 
process  of  moving  the  moon  away  from  the  earth  is  a 
cumulative  one,  going  on  century  after  century,  and  with 
reference  to  it  the  moon's  orbit  must  be  described  not  as 
a  circle  or  ellipse,  or  any  other  curve  which  returns  into 
itself,  but  as  a  spiral,  like  the  balance  spring  of  a  watch, 
each  of  whose  coils  is  a  little  larger  than  the  preceding 
one,  although  this  excess  is,  to  be  sure,  very  small,  be- 
cause the  tides  themselves  are  small  and  the  tidal  in- 
fluence feeble  when  compared  with  the  whole  attrac- 
tion of  the  earth  for  the  moon.  But^  given  time  enough, 
even  this  small  force  may  accomplish  great  results,  and 
something  like  100,000,000  years  of  past  opportunity 
would  have  sufficed  for  the  tidal  forces  to  move  the  moon 
from  close  proximity  with  the  earth  out  to  its  present  po- 
sition. 

For  millions  of  years  to  come,  if  moon  and  earth  endure 
so  long,  the  distance  between  them  must  go  on  increasing, 
although  at  an  ever  slower  rate,  since  the  farther  away  the 
moon  goes  the  smaller  will  be  the  tides  and  the  slower  the 
working  out  of  their  results.  On  the  other  hand,  when 
the  moon  was  nearer  the  earth  than  now,  tidal  influences 
must  have  been  greater  and  their  effects  more  rapidly 
produced  than  at  the  present  time,  particularly  if,  as 
seems  probable,  at  some  past  epoch  the  earth  was  hot  and 
plastic  like  Jupiter  and  Saturn.  Then,  instead  of  tides  in 
the  water  of  the  sea,  such  as  we  now  have,  the  whole  sub- 
stance of  the  earth  would  respond  to  the  moon's  attraction 
in  bodily  tides  of  semi-fluid  matter  not  only  higher,  but  with 
greater  internal  friction  of  their  molecules  one  upon  an- 


GROWTH  AND  DECAY  369 

other,  and  correspondingly  greater  effect  in  checking  the 
earth's  rotation. 

But,  whether  the  tide  be  a  bodily  one  or  confined  to  the 
waters  of  the  sea,  so  long  as  the  moon  causes  it  to  flow 
there  will  be  a  certain  amount  of  friction  which  will  affect 
the  earth  much  as  a  brake  affects  a  revolving  wheel,  slow- 
ing down  its  motion,  and  producing  thus  a  longer  day  as 
well  as  a  longer  month  on  account  of  the  moon's  increased 
distance.  Slowing  down  the  earth's  rotation  is  the  direct 
action  of  the  moon  upon  the  earth.  Pushing  the  moon 
away  is  the  form  in  which  the  earth's  equal  and  contrary 
reaction  manifests  itself. 

235.  Consequences  of  tidal  friction  upon  the  moon. — When 
the  moon  was  plastic  the  earth  must  have  raised  in  it  a 
bodily  tide  manifold  greater  than  the  lunar  tides  upon  the 
earth,  and,  as  we  have  seen  in  Chapter  IX,  this  tide  has 
long  since  worn  out  the  greater  part  of  the  moon's  rotation 
and  brought  our  satellite  to  the  condition  in  which  it  pre- 
sents always  the  same  face  toward  the  earth. 

These  two  processes,  slowing  down  the  rotation  and 
pushing  away  the  disturbing  body,  are  inseparable — one 
requires  the  other ;  and  it  is  worth  noting  in  this  connec- 
tion that  when  for  any  reason  the  tide  ceases  to  flow,  and 
the  tidal  wave  takes  up  a  permanent  position,  as  it  has  in 
the  moon  (§  99),  its  work  is  ended,  for  when  there  is  no 
motion  of  the  wave  there  can  be  no  friction  to  further 
reduce  the  rate  of  rotation  of  the  one  body,  and  no  reaction 
to  that  friction  to  push  away  the  other.  But  this  perma- 
nent and  stationary  tidal  wave  in  the  moon,  or  elsewhere, 
means  that  the  satellite  presents  always  the  same  face 
toward  its  planet,  moving  once  about  its  orbit  in  the  time 
required  for  one  revolution  upon  its  axis,  and  the  tide 
raised  by  the  moon  upon  the  earth  tends  to  produce  here 
the  result  long  since  achieved  in  our  satellite,  to  make  our 
day  and  month  of  equal  length,  and  to  make  the  earth 
turn  always  the  same  side  toward  the  moon.  But  the 


370  ASTRONOMY 

moon's  tidal  force  is  small  compared  with  that  of  the  earth, 
and  has  a  vastly  greater  momentum  to  overcome,  so  that 
its  work  upon  the  earth  is  not  yet  complete.  According 
to  Thomson  and  Tait,  the  moon  must  be  pushed  off  an- 
other hundred  thousand  miles,  and  the  day  lengthened  out 
by  tidal  influence  to  seven  of  our  present  weeks  before  the 
day  and  the  lunar  month  are  made  of  equal  length,  and 
the  moon  thereby  permanently  hidden  from  one  hemisphere 
of  the  earth. 

236.  The  earth-moon  system, — Eetracing  into  the  past 
the  course  of  development  of  the  earth  and  moon,  it  is  pos- 
sible to  reach  back  by  means  of  the  mathematical  theory 
of  tidal  friction  to  a  time  at  which  these  bodies  were  much 
nearer  to  each  other  than  now,  but  it  has  not  been  found 
possible  to  trace  out  the  mode  of  their  separation  from  one 
body  into  two,  as  is  supposed  in  the  nebular  theory.  In 
the  earliest  part  of  their  history  accessible  to  mathematical 
analysis  they  are  distinct  bodies  at  some  considerable  dis- 
tance from  each  other,  with  the  earth  rotating  about  an 
axis  more  nearly  perpendicular  to  the  moon's  orbit  and  to 
the  ecliptic  than  is  now  the  case.  Starting  from  such  a 
condition,  the  lunar  tides,  according  to  Darwin,  have  been 
instrumental  in  tipping  the  earth's  rotation  axis  into  its 
present  oblique  position,  and  in  determining  the  eccen- 
tricity of  the  moon's  orbit  and  its  position  with  respect  to 
the  ecliptic  as  well  as  the  present  length  of  day  and  month. 

337.  Tidal  friction  upon  the  planets. — The  satellites  of  the 
outer  planets  are  equally  subject  to  influences  of  this  kind, 
and  there  appears  to  be  independent  evidence  that  some  of 
them,  at  least,  turn  always  the  same  face  toward  their 
respective  planets,  indicating  that  the  work  of  tidal  friction 
has  here  been  accomplished.  We  saw  in  Chapter  XI  that 
it  is  at  present  an  open  question  whether  the  inner  planets, 
Venus  and  Mercury,  do  not  always  turn  the  same  face 
toward  the  sun,  their  day  and  year  being  of  equal  length. 
In  addition  to  the  direct  observational  evidence  upon  this 


GKOWTH  AND  DECAY  371 

point,  Schiaparelli  has  sought  to  show  by  an  appeal  to  tidal 
theory  that  such  is  probably  the  case,  at  least  for  Mercury, 
since  the  tidal  forces  which  tend  to  bring  about  this  result 
in  that  planet  are  about  as  great  as  the  forces  which  have 
certainly  produced  it  in  the  case  of  the  moon  and  Saturn's 
satellite,  Japetus.  The  same  line  of  reasoning  would  show 
that  every  satellite  in  the  solar  system,  save  possibly  the 
newly  discovered  ninth  satellite  of  Saturn,  must,  as  a  con- 
sequence of  tidal  friction,  turn  always  the  same  face  toward 
its  planet. 

238.  The  solar  tide, — The  sun  also  raises  tides  in  the 
earth,  and  their  influence  must  be  similar  in  character  to 
that  of  the  lunar  tides,  checking  the  rotation  of  the  earth 
and  thrusting  earth  and  sun  apart,  although  quantitatively 
these  effects  are  small  compared  with  those  of  the  moon. 
They  must,  however,  continue  so  long  as  the  solar  tide 
lasts,  possibly  until  the  day  and  year  are  made  of  equal 
length — i.  e.,  they  may  continue  long  after  the  lunar  tidal 
influence  has  ceased  to  push  earth  and  moon  apart.     Should 
this  be  the  case,  a  curious  inverse  effect  will  be  produced. 
The  day  being  then  longer  than  the  month,  the  moon  will 
again  raise  a  tide  in  the  earth  which  will  run  around  it 
from  west  to  east,  opposite  to  the  course  of  the  present  tide, 
thus  tending  to  accelerate  the  earth's  rotation,  and  by  its 
reaction  to  bring  the  moon  back  toward  the  earth  again, 
and  ultimately  to  fall  upon  it. 

We  may  note  that  an  effect  of  this  kind  must  be  in 
progress  now  between  Mars  and  its  inner  satellite,  Phobos, 
whose  time  of  orbital  revolution  is  only  one  third  of  a  Mar- 
tian day.  It  seems  probable  that  this  satellite  is  in  the  last 
stages  of  its  existence  as  an  independent  body,  and  must 
ultimately  fall  into  Mars. 

239.  Roche's  limit— In  looking  forward  to  such  a  catas- 
trophe, however,  due  regard  must  be  paid  to  a  dynamical 
principle  of  a  different  character.     The  moon  can  never  be 
precipitated  upon  the  earth  entire,  since  before  it  reaches 


372  ASTRONOMY 

us  it  will  have  been  torn  asunder  by  the  excess  of  the 
earth's  attraction  for  the  near  side  of  its  satellite  over  that 
which  it  exerts  upon  the  far  side.  As  the  result  of  Eoche's 
mathematical  analysis  we  are  able  to  assign  a  limiting  dis- 
tance between  any  planet  and  its  satellite  within  which  the 
satellite,  if  it  turns  always  the  same  face  toward  the  planet, 
can  not  come  without  being  broken  into  fragments.  If  we 
represent  the  radius  of  the  planet  by  r,  and  the  quotient 
obtained  by  dividing  the  density  of  the 'planet  by  the  den- 
sity of  the  satellite  by  <?,  then 

Eoche's  limit  =  2.44  r  l/q. 

Thus  in  the  case  of  earth  and  moon  we  find  from  the  den- 
sities given  in  §  95,  q  =  1.65,  and  with  r  =  3,963  miles  we 
obtain  11,400  miles  as  the  nearest  approach  which  the  moon 
could  make  to  the  earth  without  being  broken  up  by  the 
difference  of  the  earth's  attractions  for  its  opposite  sides. 

We  must  observe,  however,  that  Eoche's  limit  takes  no 
account  of  molecular  forces,  the  adhesion  of  one  molecule 
to  another,  by  virtue  of  which  a  stick  or  stone  resists  frac- 
ture, but  is  concerned  only  with  the  gravitative  forces  by 
which  the  molecules  are  attracted  toward  the  moon's  center 
and  toward  the  earth.  Within  a  stone  or  rock  of  moderate 
size  these  gravitative  forces  are  insignificant,  and  cohesion 
is  the  chief  factor  in  preserving  its  integrity,  but  in  a  large 
body  like  the  moon,  the  case  is  just  reversed,  cohesion  plays 
a  small  part  and  gravitation  a  large  one  in  holding  the 
body  together.  We  may  conclude,  therefore,  that  at  a 
proper  distance  these  forces  are  capable  of  breaking  up  the 
moon,  or  any  other  large  body,  into  fragments  of  a  size 
such  that  molecular  cohesion  instead  of  gravitation  is  the 
chief  agent  in  preserving  them  from  further  disintegration. 

240.  Saturn's  rings. — Saturn's  rings  are  of  peculiar  in- 
terest in  this  connection.  The  outer  edge  of  the  ring  sys- 
tem lies  just  inside  of  Eoche's  limit  for  this  planet,  and  we 
have  already  seen  that  the  rings  are  composed  of  small  frag- 


GROWTH   AND  DECAY  3Y3 

ments  independent  of  each  other.  Whatever  may  have 
been  the  process  by  which  the  nine  satellites  of  Saturn 
came  into  existence,  we  have  in  Eoche's  limit  the  explana- 
tion why  the  material  of  the  ring  was  not  worked  up  into 
satellites ;  the  forces  exerted  by  Saturn  would  tear  into 
pieces  any  considerable  satellite  thus  formed  and  equally 
would  prevent  the  formation  of  one  from  raw  material. 

Saturn's  rings  present  the  only  case  within  the  solar 
system  where  matter  is  known  to  be  revolving  about  a 
planet  at  a  distance  less  than  Roche's  limit,  and  it  is  an 
interesting  question  whether  these  rings  can  remain  as  a 
permanent  part  of  the  planet's  system  or  are  only  a  tempo- 
rary feature.  The  drawings  of  Saturn  made  two  centuries 
ago  agree  among  themselves  in  representing  the  rings  as 
larger  than  they  now  appear,  and  there  is  some  reason  to 
suppose  that  as  a  consequence  of  mutual  disturbances — col- 
lisions— their  momentum  is  being  slowly  wasted  so  that 
ultimately  they  must  be  precipitated  into  the  planet.  But 
the  direct  evidence  of  such  a  progress  that  can  be  drawn 
from  present  data  is  too  scanty  to  justify  positive  conclu- 
sions in  the  matter.  On  the  other  hand,  Xolan  suggests 
that  in  the  outer  parts  of  the  ring  small  satellites  might  be 
formed  whose  tidal  influence  upon  Saturn  would  suffice  to 
push  them  away  from  the  ring  beyond  Roche's  limit,  and 
that  the  very  small  inner  satellites  of  Saturn  may  have 
been  thus  formed  at  the  expense  of  the  ring. 

The  inner  satellite  of  Mars  is  very  close  to  Roche's  limit 
for  that  planet,  and,  as  we  have  seen  above,  must  be  approach- 
ing still  nearer  to  the  danger  line. 

241.  The  moon's  development— The  fine  series  of  photo- 
graphs of  the  moon  obtained  within  the  last  few  years  at 
Paris,  have  been  used  by  the  astronomers  of  that  observa- 
tory for  a  minute  study  of  the  lunar  formations,  much  as 
geologists  study  the  surface  of  the  earth  to  determine  some- 
thing about  the  manner  in  which  it  was  formed.  Their 
conclusions  are,  in  general,  that  at  some  past  time  the  moon 


374:  ASTRONOMY 

was  a  hot  and  fluid  body  which,  as  it  cooled  and  condensed, 
formed  a  solid  crust  whose  further  shrinkage  compressed 
the  liquid  nucleus  and  led  to  a  long  series  of  fractures  in 
the  crust  and  outbursts  of  liquid  matter,  whose  latest  and 
feeblest  stages  produced  the  lunar  craters,  while  traces  of 
the  earlier  ones,  connected  with  a  general  settling  of  the 
crust,  although  nearly  obliterated,  are  still  preserved  in  cer- 
tain large  but  vague  features  of  the  lunar  topography,  such 
as  the  distribution  of  the  seas,  etc.  They  find  also  in  cer- 
tain markings  of  the  surface  what  they  consider  convincing 
evidence  of  the  existence  in  past  times  of  a  lunar  atmos- 
phere. But  this  seems  doubtful,  since  the  force  of  gravity 
at  the  moon's  surface  is  so  small  that  an  atmosphere  similar 
to  that  of  the  earth,  even  though  placed  upon  the  moon, 
could  not  permanently  endure,  but  would  be  lost  by  the 
gradual  escape  of  its  molecules  into  the  surrounding  space. 
The  molecules  of  a  gas  are  quite  independent  one  of 
another,  and  are  in  a  state  of  ceaseless  agitation,  each  one 
darting  to  and  fro,  colliding  with  its  neighbors  or  with 
whatever  else  opposes  its  forward  motion,  and  traveling 
with  velocities  which,  on  the  average,  amount  to  a  good 
many  hundreds  of  feet  per  second,  although  in  the  case  of 
any  individual  molecule  they  may  be  much  less  or  much 
greater  than  the  average  value,  an  occasional  molecule  hav- 
ing possibly  a  velocity  several  times  as  great  as  the  average. 
In  the  upper  regions  of  our  own  atmosphere,  if  one  of  these 
swiftly  moving  particles  of  oxygen  or  nitrogen  were  headed 
away  from  the  earth  with  a  velocity  of  seven  miles  per  sec- 
ond, the  whole  attractive  power  of  the  earth  would  be 
insufficient  to  check  its  motion,  and  it  would  therefore, 
unless  stopped  by  some  collision,  escape  from  the  earth  and 
return  no  more.  But,  since  this  velocity  of  seven  miles  per 
second  is  more  than  thirty  times  as  great  as  the  average 
velocity  of  the  molecules  of  air,  it  must  be  very  seldom  in- 
deed that  one  is  found  to  move  so  swiftly,  and  the  loss  of 
the  earth's  atmosphere  by  leakage  of  this  sort  is  insignifi- 


GROWTH  AND  DECAY  375 

cant.  But  upon  the  moon,  or  any  other  body  where  the 
force  of  gravity  is  small,  conditions  are  quite  different,  and 
in  our  satellite  a  velocity  of  little  more  than  one  mile  per 
second  would  suffice  to  carry  a  molecule  away  from  the 
outer  limits  of  its  atmosphere.  This  velocity,  only  five  times 
the  average,  would  be  frequently  attained,  particularly  in 
former  times  when  the  moon's  temperature  was  high,  for 
then  the  average  velocity  of  all  the  molecules  would  be  con- 
siderably increased,  and  the  amount  of  leakage  might  be- 
come, and  probably  would  become,  a  serious  matter,  steadi- 
ly depleting  the  moon's  atmosphere  and  leading  finally  to 
its  present  state  of  exhaustion.  It  is  possible  that  the 
moon  may  at  one  time  have  had  an  atmosphere,  but  if  so  it 
could  have  been  only  a  temporary  possession,  and  the  same 
line  of  reasoning  may  be  applied  to  the  asteroids  and  to 
most  of  the  satellites  of  the  solar  system,  and  also,  though 
in  less  degree,  to  the  smaller  planets,  Mercury  and  Mars. 

242.  Stellar  development. — We  have  already  considered 
in  this  chapter  the  line  of  development  followed  by  one 
star,  the  sun,  and  treating  this  as  a  typical  case,  it  is  com- 
monly believed  that  the  life  history  of  a  star,  in  so  far  as  it 
lies  within  our  reach,  begins  with  a  condition  in  which  its 
matter  is  widely  diffused,  and  presumably  at  a  low  tempera- 
ture. Contracting  in  bulk  under  the  influence  of  its  own 
gravitative  forces,  the  star's  temperature  rises  to  a  maxi- 
mum, and  then  falls  off  in  later  stages  until  the  body  ceases 
to  shine  and  passes  over  to  the  list  of  dark  stars  whose 
existence  can  only  be  detected  in  exceptional  cases,  such 
as  are  noted  in  Chapter  XIII.  The  most  systematic  devel- 
opment of  this  idea  is  due  to  Lockyer,  who  looks  upon  all 
the  celestial  bodies — sun,  moon  and  planets,  stars,  nebulae, 
and  comets — as  being  only  collections  of  meteoric  matter  in 
different  stages  of  development,  and  who  has  sought  by 
means  of  their  spectra  to  classify  these  bodies  and  to  deter- 
mine their  stage  of  advancement.  While  the  fundamental 
ideas  involved  in  this  "  meteoritic  hypothesis  "  are  not  seri- 


376  ASTRONOMY 

ously  controverted,  the  detailed  application  of  its  principles 
is  open  to  more  question,  and  for  the  most  part  those 
astronomers  who  hold  that  in  the  present  state  of  knowl- 
edge stellar  spectra  furnish  a  key  to  a  star's  age  or  degree 
of  advancement  do  not  venture  beyond  broad  general  state- 
ments. 

24:3.  Stellar  spectra.— Thus  the  types  of  stellar  spectra 
shown  in  Fig.  151  are  supposed  to  illustrate  successive 
stages  in  the  development  of  an  average  star.  Type  I  cor- 


FIG.  151. — Types  of  stellar  spectra  substantially  according  to  SECCHT. 

responds  to  the  period  in  which  its  temperature  is  near  the 
maximum ;  Type  II  belongs  to  a  later  stage  in  which  the 
temperature  has  commenced  to  fall ;  and  Type  III  to  the 
period  immediately  preceding  extinction. 

While  human  life,  or  even  the  duration  of  the  human 
race,  is  too  short  to  permit  a  single  star  to  be  followed 
through  all  the  stages  of  its  career,  an  adequate  picture  of 
that  development  might  be  obtained  by  examining  many 
stars,  each  at  a  different  stage  of  progress,  and,  following 


GROWTH   AND  DECAY  377 

this  idea,  numerous  subdivisions  of  the  types  of  stellar 
spectra  shown  in  Fig.  151  have  been  proposed  in  order  to 
represent  with  more  detail  the  process  of  stellar  growth 
and  decay  ;  but  for  the  most  part  these  subdivisions  and 
their  interpretation  are  accepted  by  astronomers  with  much 
reserve. 

It  is  significant  that  there  are  comparatively  few  stars 
with  spectra  of  Type  III,  for  this  is  what  we  should  expect 
to  find  if  the  development  of  a  star  through  the  last  stages 
of  its  visible  career  occupied  but  a  small  fraction  of  its 
total  life.  From  the  same  point  of  view  the  great  number 
of  stars  with  spectra  of  the  first  type  would  point  to  a  long 
duration  of  this  stage  of  life.  The  period  in  which  the 
sun  belongs,  represented  by  TjTpe  II,  probably  has  a  dura- 
tion intermediate  between  the  others.  Since  most  of  the 
variable  stars,  save  those  of  the  Algol  class,  have  spectra  of 
the  third  type,  we  conclude  that  variability,  with  its  associ- 
ated ruddy  color  and  great  atmospheric  absorption  of  light, 
is  a  sign  of  old  age  and  approaching  extinction.  The  Algol 
or  eclipse  variables,  on  the  other  hand,  having  spectra  of  the 
first  type,  are  comparatively  young  stars,  and,  as  we  shall 
see  a  little  later,  the  shortness  of  their  light  periods  in  some 
measure  confirms  this  conclusion  drawn  from  their  spectra. 

We  have  noted  in  §  196  that  the  sun's  near  neighbors 
are  prevailingly  stars  with  spectra  of  the  second  type, 
while  the  Milky  Way  is  mainly  composed  of  first-type  stars, 
and  from  this  we  may  now  conclude  that  in  our  particular 
part  of  the  entire  celestial  space  the  stars  are,  as  a  rule, 
somewhat  further  developed  than  is  the  case  elsewhere. 

244.  Double  stars. — The  double  stars  present  special 
problems  of  development  growing  out  of  the  effects  of  tidal 
friction,  which  must  operate  in  them  much  as  it  does  be- 
tween earth  and  moon,  tending  steadily  to  increase  the  dis- 
tance between  the  components  of  such  a  star.  So,  too, 
in  such  a  system  as  is  shown  in  Fig.  133,  gravity  must 
tend  to  make  each  component  of  the  double  star  shrink  to 
25 


378  ASTRONOMY 

smaller  dimensions,  and  this  shrinkage  must  result  in 
faster  rotation  and  increased  tidal  friction,  which  in  turn 
must  push  the  components  apart,  so  that  in  view  of  the 
small  density  and  close  proximity  of  those  particular  stars 
we  may  fairly  regard  a  star  like  {3  Lyrae  as  in  the  early  stages 
of  its  career  and  destined  with  increasing  age  to  lose  its 
variability  of  light,  since  the  eclipses  which  now  take  place 
must  cease  with  increasing  distance  between  the  compo- 
nents unless  the  orbit  is  turned  exactly  edgewise  toward  the 
earth.  Close  proximity  and  the  resulting  shortness  of  pe- 
riodic time  in  a  double  star  seem,  therefore,  to  be  evidence 
of  its  youth,  and  since  this  shortness  of  periodic  time  is 
characteristic  of  both  Algol  variables  and  spectroscopic 
binaries  as  a  class,  we  may  set  them  down  as  being,  upon 
the  whole,  stars  in  the  early  stages  of  their  career.  On 
the  other  hand,  it  is  generally  true  that  the  larger  the  or- 
bit, and  the  greater  the  periodic  time  in  the  orbit,  the 
farther  is  the  star  advanced  in  its  development. 

In  his  theory  of  tidal  friction,  Darwin  has  pointed  out 
that  whenever  the  periodic  time  in  the  orbit  is  more  than 
twice  as  long  as  the  time  required  for  rotation  about  the 
axis,  the  effect  of  the  tides  is  to  increase  the  eccentricity  of 
the  orbit,  and,  following  this  indication,  See  has  urged  that 
with  increasing  distance  between  the  components  of  a 
double  star  their  orbits  about  the  common  center  of  grav- 
ity must  grow  more  and  more  eccentric,  so  that  we  have  in 
the  shape  of  such  orbits  a  new  index  of  stellar  develop- 
ment ;  the  more  eccentric  the  orbit,  the  farther  advanced 
are  the  stars.  It  is  important  to  note  in  this  connection 
that  among  the  double  stars  whose  orbits  have  been  com- 
puted there  seems  to  run  a  general  rule — the  larger  the 
orbit  the  greater  is  its  eccentricity— a  relation  which  must 
hold  true  if  tidal  friction  operates  as  above  supposed,  and 
which,  being  found  to  hold  true,  confirms  in  some  degree 
the  criteria  of  stellar  age  which  are  furnished  by  the  theory 
of  tidal  friction. 


GROWTH  AND  DECAY  379 

245.  Nebulae, — The  nebular  hypothesis  of  Laplace  has 
inclined  astronomers  to  look  upon  nebulae  in  general  as 
material  destined  to  be  worked  up  into  stars,  but  which  is 
now  in  a  very  crude  and  undeveloped  stage.     Their  great 
bulk  and  small  density  seem  also  to  indicate  that  gravitation 
has  not  yet  produced  in  them  results  at  all  comparable  with 
what  we  see  in  sun  and  stars.     But  even  among  nebulae 
there  are  to  be  found  very  different  stages  of  development. 
The    irregular   nebula,   shapeless   and   void    like   that   of 
Orion ;  the  spiral,  ring,  and  planetary  nebulas  and  the  star 
cluster,  clearly  differ  in  amount  of  progress  toward  their 
final  goal.     But  it  is  by  no  means  sure  that  these  several 
types  are  different  stages  in  one  line  of  development ;  for 
example,  the  primitive  nebula  which  grows  into  a  spiral 
may  never  become  a  ring  or  planetary  nebula,  and  vice 
versa.     So  too  there  is  no  reason  to  suppose  that  a  star 
cluster  will  ever  break  up  into  isolated  stars  such  as  those 
whose  relation  to  each  other  is  shown  in  Fig.  122. 

246.  Classification. — Considering    the    heavenly    bodies 
with  respect  to  their  stage  of  development,  and  arranging 
them  in  due  order,  we  should  probably  find  lowest  down  in 
the  scale  of  progress  the  irregular  nebula  of  chaotic  ap- 
pearance such  as  that  represented  in   Fig.    146.      Above 
these  in  point  of  development  stand  the  spiral,  ring,  and 
planetary  nebulae,  although  the  exact  sequence  in  which 
they  should  be  arranged  remains  a  matter  of  doubt.     Still 
higher,  up  in  the  scale  are  star  clusters  whose  individual 
members,  as  well  as  isolated  stars,  are  to  be  classified  by 
means  of  their  spectra,  as  shown  in  Fig.  151,  where  the 
order  of  development  of  each  star  is  probably  from  Type  I, 
through  II,  into  III  and  beyond,  to  extinction  of  its  light 
and  the  cutting  off  of  most  of  its  radiant  energy.     Jupiter 
and  Saturn  are  to  be  regarded  as  stars  which  have  recently 
entered  this  dark  stage.     The  earth  is  further  developed 
than  these,  but  it  is  not  so  far  along  as  are  Mars  and  Mer- 
cury ;  while  the  moon  is  to  be  looked  upon  as  the  most 


380  ASTRONOMY 

advanced  heavenly  body  accessible  to  our  research,  having 
reached  a  state  of  decrepitude  which  may  almost  be  called 
death— a  stage  typical  of  that  toward  which  all  the  others 
are  moving. 

Meteors  and  comets  are  to  be  regarded  as  fragments  of 
celestial  matter,  chips,  too  small  to  achieve  by  themselves 
much  progress  along  the  normal  lines  of  development,  but 
destined  sooner  or  later,  by  collision  with  some  larger  body, 
to  share  thenceforth  in  its  fortunes. 

247.  Stability  of  the  universe, — It  was  considered  a  great 
achievement  in  the  mathematical  astronomy  of  a  century 
ago  when  Laplace  showed  that  the  mutual  attractions  of 
sun  and  planets  might  indeed  produce  endless  perturba- 
tions in  the  motions  and  positions  of  these  bodies,  but 
could  never  bring  about  collisions  among  them  or  greatly 
alter  their  existing  orbits.  But  in  the  proof  of  this  great 
theorem  two  influences  were  neglected,  either  of  which  is 
fatal  to  its  validity.  One  of  these — tidal  friction — as  we 
have  already  seen,  tends  to  wreck  the  systems  of  satellites, 
and  the  same  effect  must  be  produced  upon  the  planets  by 
any  other  influence  which  tends  to  impede  their  orbital 
motion.  It  is  the  inertia  of  the  planet  in  its  forward  move- 
ment that  balances  the  sun's  attraction,  and  any  diminu- 
tion of  the  planet's  velocity  will  give  this  attraction  the 
upper  hand  and  must  ultimately  precipitate  the  planet 
into  the  sun.  The  meteoric  matter  with  which  the  earth 
comes  ceaselessly  into  collision  must  have  just  this  influ- 
ence, although  its  effects  are  very  small,  and  some- 
thing of  the  same  kind  may  come  from  the  medium 
which  transmits  radiant  energy  through  the  interstellar 
spaces. 

It  seems  incredible  that  the  luminiferous  ether,  which 
is  supposed  to  pervade  all  space,  should  present  absolutely 
no  resistance  to  the  motion  of  stars  and  planets  rushing 
through  it  with  velocities  which  in  many  cases  exceed 
50,000  miles  per  hour.  If  there  is  a  resistance  to  this  mo- 


GROWTH  AND  DECAY  381 

tion,  however  small,  we  may  extend  to  the  whole  visible 
universe  the  words  of  Thomson  and  Tait,  who  say  in  their 
great  Treatise  on  Katural  Philosophy, "  We  have  no  data  in 
the  present  state  of  science  for  estimating  the  relative  im- 
portance of  tidal  friction  and  of  the  resistance  of  the  resist- 
ing medium  through  which  the  earth  and  moon  move ; 
but,  whatever  it  may  be,  there  can  be  but  one  ultimate 
result  for  such  a  system  as  that  of  the  sun  and  planets, 
if  continuing  long  enough  under  existing  laws  and  not 
disturbed  by  meeting  with  other  moving  masses  in 
space.  That  result  is  the  falling  together  of  all  into 
one  mass,  which,  although  rotating  for  a  time,  must  in 
the  end  come  to  rest  relatively  to  the  surrounding  me- 
dium." 

Compare  with  this  the  words  of  a  great  poet  who  in 
The  Tempest  puts  into  the  mouth  of  Prospero  the  lines : 

"  The  cloud-capp'd  towers,  the  gorgeous  palaces, 
The  solemn  temples,  the  great  globe  itself, 
Yea,  all  which  it  inherit,  shall  dissolve  ; 
And,  like  this  insubstantial  pageant  faded, 
Leave  not  a  rack  behind." 

248.  The  future. — In  spite  of  statements  like  these,  it 
lies  beyond  the  scope  of  scientific  research  to  affirm  that 
the  visible  order  of  things  will  ever  come  to  naught,  and 
the  outcome  of  present  tendencies,  as  sketched  above,  may 
be  profoundly  modified  in  ages  to  come,  by  influences  of 
which  we  are  now  ignorant.  We  have  already  noted  that 
the  farther  our  speculation  extends  into  either  past  or 
future,  the  more  insecure  are  its  conclusions,  and  the  re- 
moter consequences  of  present  laws  are  to  be  accepted  with 
a  corresponding  reserve.  But  the  one  great  fact  which 
stands  out  clear  in  this  connection  is  that  of  change.  The 
old  concept  of  a  universe  created  in  finished  form  and  des- 
tined so  to  abide  until  its  final  dissolution,  has  passed  away 
from  scientific  thought  and  is  replaced  by  the  idea  of  slow 


382  ASTRONOMY 

development.  A  universe  which  is  ever  becoming  some- 
thing else  and  is  never  finished,  as  shadowed  forth  by 
Goethe  in  the  lines  : 

"  Thus  work  I  at  the  roaring  loom  of  Time, 
And  weave  for  Deity  a  living  robe  sublime  " 


APPENDIX 


THE  GEEEK  ALPHABET 

THE  Greek  letters  are  so  much  used  by  astronomers  in 
connection  with  the  names  of  the  stars,  and  for  other  pur- 
poses, that  the  Greek  alphabet  is  printed  below — not  neces- 
sarily to  be  learned,  but  for  convenient  reference  : 

Greek. 
A  a 

B  ft 

r         7 

A  d 

E  e  or  e 

Z  f 

H  T, 

e  #  or  6 

1  i 
K  K 
A  X 
M  /A 
N  v 
»  I 
O  o 

n         TT 

p       p 

2  a-  or  $• 
T  T 

Y  v 


Name. 

English. 

Alpha 

a 

Beta 

b 

Gamma 

g 

Delta 

d 

Epsilon 

6 

Zeta 

z 

Eta 

e 

Theta 

th 

Iota 

i 

Kappa 

k 

Lambda 

1 

Mu 

m 

Nu 

n 

Xi 

X 

Omicron 

6 

Pi 

P 

Rho 

r 

Sigma 

s 

Tau 

t 

Upsilon 

u 

Phi 

ph 

Chi 

ch 

Psi 

ps 

Omega 

6 

383 

384  ASTRONOMY 


POPULAE  LlTEEATUEE  OF  ASTEONOMY 

THE  following  brief  bibliography,  while  making  no 
pretense  at  completeness,  may  serve  as  a  useful  guide  to 
supplementary  reading : 

General  Treatises 

^  YOUNG.  General  Astronomy.  An  admirable  general  survey  of  the 
entire  field. 

V  NEWCOMB.  Popular  Astronomy.  The  second  edition  of  a  German 
translation  of  this  work  by  Engelmann  and  Vogel  is  especially  valuable. 

v  BALL.  Story  of  the  Heavens.  Somewhat  easier  reading  than  either 
of  the  preceding. 

v  CHAMBERS.  Descriptive  Astronomy.  An  elaborate  but  elementary 
work  in  three  volumes. 

vLANGLEY.  The  New  Astronomy.  Treats  mainly  of  the  physical 
condition  of  the  celestial  bodies. 

/PROCTOR  and  RANYARD.     Old  and  New  Astronomy. 

Special  Treatises 

PROCTOR.     The  Noon.     A  general  treatment  of  the  subject. 
NASMYTH  and  CARPENTER.     The  Moon.     An  admirably  illustrated 
but  expensive  work  dealing  mainly  with  the  topography  and  physical 
conditions  of  the  moon.     There  is  a  cheaper  and  very  good  edition  in 
German. 

v  YOUNG.  The  Sun.  International  Scientific  Series.  The  most  recent 
and  authoritative  treatise  on  this  subject. 

"  PROCTOR.  Other  Worlds  than  Ours.  An  account  of  planets,  com- 
ets, etc. 

NEWTON.     Meteor.     Encyclopaedia  Britannica. 
AIRY.     Gravitation.     A  non-mathematical  exposition  of  the  laws 
of  planetary  motion. 

^  STOKES.     On  Light  as  a  Means  of  Investigation.     Burnett  Lectures. 
II.     The  basis  of  spectrum  analysis. 
^CHELLEN.     Spectrum  Analysis. 

V/THOMSON  (Sir  W.,  Lord  KELVIN),  Popular  Lectures,  etc.  Lectures 
on  the  Tides,  The  Sun's  Heat,  etc. 


APPENDIX  385 

Time  and  Tide.    An  exposition  of  the  researches  of  G.  H. 
Darwin  upon  tidal  friction.    , 

GORE.     The  Visible  Universe.     Deals  with  a  class  of  problems  inad- 
equately treated  in  most  popular  astronomies. 
y  DARWIN.     The  Tides.     An  admirable  elementary  exposition. 
^CLERKE.     The  System  of  the  Stars.     Stellar  astronomy. 

NEWCOMB.     Chapters  on  the  Stars,  in  Popular  Science  Monthly  for 
1900. 

CLERKE.    History  of  Astronomy  during  the  Nineteenth  Century. 
An  admirable  work. 

WOLF.     Geschichte  der  Astronomic.     Mlinchen,  1877.    An  excellent 
German  work. 


386 


ASTRONOMY 


A  LIST  OF  STARS  FOR  TIME  OBSERVATIONS 

See  8  20. 


NAME. 

Magnitude. 

Right  Ascension. 

Declination. 

0  Ceti             

2 

h.      m. 

0  38.6 

0 

—  18.5 

77  Ceti  

3 

1    3.6 

—  10.7 

a  Ceti  

3 

2  57.1 

+   3.7 

y  Eridani      .       

3 

3  53.4 

—  13  8 

Aldebaran     

1 

4  30.2 

4  16.3 

Rig  el 

0 

5    9.7 

—  8.3 

K  Orioriis  

2 

5  43.0 

—  9.7 

2 

6  18.3 

—17.9 

Siviiis 

_1 

6  40  7 

—16.6 

Procyon                    

0 

7  34.1 

+   5.5 

ct  HvdrsB 

2 

9  22.7 

—  8.2 

Reoulus             .       

1 

10    3.0 

+  12.5 

v  HydraB    

3 

10  44.7 

-15.7 

3 

12    5.0 

-22.1 

y  Corvi                      .        .    . 

3 

12  10.7 

-17.0 

Spica    

1 

13  19.9 

-10.6 

(*  Virsrinis             •  , 

3 

13  29.6 

-  0.1 

a  Librae          

3 

14  45.3 

-15.6 

)8  LibraB      

3 

15  11.6 

-  9.0 

Antarcs                    .     ... 

1 

16  23.3 

-26.2 

2 

17  30.3 

+  12.6 

e  Sagittarii  

2 

18  17.5 

-34.4 

3 

19  20.5 

+  2.9 

Altair             

1 

19  45.9 

+  8.6 

/8  Aquarii  

3 

21  26.3 

-  6.0 

3 

22    0.6 

-  0.8 

FoTtmlhciut                    .  . 

1 

22  52.1 

-30.2 

INDEX 


The  references  are  to  section  numbers. 


Absorption  of  starlight,  225. 
Absorption  spectra,  87. 
Accelerating  force,  35. 
Adjustment  of  observations,  2. 
Albedo  of  moon,  97. 

of  Venus,  148. 
Algol,  205. 
Altitudes,  4,  21. 
Andromeda  nebula,  214. 
Angles,  measurement  of,  2. 
Angular  diameter,  7. 
Annular  eclipse,  64. 
Asteroids,  156. 
Atmosphere  of  the  earth,  49. 

of  the  moon,  103. 

of  Jupiter,  139. 

of  Mars,  153. 
Aurora,  51. 
Azimuth,  5,  21. 

Biela's  comet,  181. 
Bode's  law,  134,  232. 
Bredichin's  theory  of  comet  tails, 
180. 

Calendar,  0.  S.  and  N.  S.,  61. 
Capture  of  comets   and   meteors, 

176. 

Canals  of  Mars,  154. 
Celestial  mechanics,  32. 
Changes  upon  the  moon,  108. 


Chemical  constitution  of  sun,  116. 

of  stars,  210. 

Chromosphere,  the  sun's,  124. 
Chronology,  59. 
Classification  of  stars,  212. 
Clocks  and  watches,  74. 

sidereal  clock,  12. 
Collisions  with  comets,  183. 
Colors  of  stars,  209. 
Comets,    general    characteristics, 
158-164. 

development  of,  179,  181. 

groups,  177. 

orbits,  161. 

periodic,  176. 

spectra,  182. 

tails,  180. 
Comets  and  meteors,  relation  of, 

175. 

Conic  sections,  38. 
Constellations,  184. 
Corona,  the  sun's,  123. 
Craters,  lunar,  105. 

Dark  stars,  201. 
Day,  52,  62. 
Declination,  21. 
Development  of  comet,  179. 

of  moon,  241. 

of  nebulae,  245. 

of  stars,  242,  244. 
387 


388 


ASTRONOMY 


Development  of  sun,  228. 

of  universe,  226. 
Distribution  of  stars  and  nebulae, 

220. 

Diurnal  motion,  10,  15. 
Doppler  principle,  89. 
Double  nebulae,  215. 
Double  stars,  198. 

development  of,  244. 
Driving  clock,  80. 

Earth,  atmosphere,  48. 

mass,  45. 

size  and  shape,  44. 

warming  of  the  earth,  47. 
Eclipses,  nature  of,  63. 

annular  eclipse,  64. 

eclipse  limits,  68. 

eclipse  maps,  70,  71. 

number  of,  in  a  year,  69. 

partial  eclipse,  64. 

prediction  of,  70,  71. 

recurrence  of,  72. 

shadow  cone,  64,  66. 

total  eclipse,  64. 

uses  of,  73. 

Eclipses  of  Jupiter's  satellites,  141. 
Eclipse  theory  of   variable  stars, 

205. 
Ecliptic,  26. 

obliquity  of,  25. 
Ellipse,  33. 

Epochs  for  planetary  motion,  30. 
Energy,  radiant,  75. 

condensation  of,  76. 
Epicycle,  32. 
Equation  of  time,  53. 
Equator,  16,  21. 
Equatorial  mounting,  80. 
Equinoxes,  25. 
Ether,  75. 
Evening  star,  31. 


Faculae,  122. 

Falling  bodies,  law  of,  35. 
Finding  the  stars,  14. 
Fraunhofer  lines,  87. 

Galaxy,  219. 

Geography  of  the  sky,  16. 
Graphical  representation,  6. 
Grating,  diffraction,  84. 
Gravitation,  law  of,  37. 

Harvest  moon,  93. 

Heat  of  the  sun,  118,  126. 

Helmholtz,  contraction  theory  of 

the  sun,  126,  228. 
Horizon,  4,  21. 
Hour  angle,  21. 
Hour  circle,  21. 
Hyperbola,  38. 

Japetus,  satellite  of  Saturn,  145. 
Jupiter,  136. 

atmosphere,  139. 

belts,  137. 

invisible  from  fixed  stars,  197. 

orbit  of,  29. 

physical  condition,  139. 

rotation  and  flattening,  138. 

satellites,  140. 

surface  markings,  137. 

Kepler's  laws,  33,  111. 

Latitude,  determination  of,  18. 

Leap  year,  61. 

Lenses,  77. 

Leonid  meteor  shower,  172. 

perturbations  of,  174. 
Librations  of  moon,  98. 
Life  upon  the  planets,  157. 
Light  curves,  205. 
Light,  nature  of,  75. 


INDEX 


389 


Light  year,  190. 
Limits  of  eclipses,  68. 
Longitude,  56. 

determination  of,  58. 
Lunation,  60. 

Magnifying    power    of    telescope, 

79. 

Magnitude,  stellar,  9,  186. 
Mars,    atmosphere,     temperature, 
150. 

canals,  154. 

orbit,  30. 

polar  caps,  152. 

rotation,  151. 

satellites,  155. 

surface  markings,  150. 
Mass,  determination  of,  37. 

of  .comets,  164. 

of  double  stars,  200. 

of  moon,  94. 

of  planets,  40,  133. 
Measurements,  accurate,  1. 
Mercury,  149. 

motion  of  its  perihelion,  43. 

orbit  of,  30. 
Meridian,  19,  21. 
Meteors,  nature  of,  165,  169. 

number  of,  167. 

velocity,  170. 
Meteors  and  comets,  relation  of, 

175. 
Meteor  showers,  radiant,  171. 

Leonids,  capture  of,  172,  173. 

perturbations,  174. 
Milky  Way,  219. 
Mira,  o  Ceti,  204. 
Mirrors,  77. 
Month,  60. 
Moon,  91. 

albedo,  97. 

atmosphere,  103. 


Moon,  changes  in,  108. 

density,  surface  gravity,  95. 

development  of,  241. 

harvest  moon,  93. 

influence  upon  the  earth,   109, 
233. 

librations,  98. 

map  of,  101. 

mass  and  size,  94. 

motion,  24,  92. 

mountains  and  craters,  104. 

phases,  91,  92. 

physical  condition,  100,  107. 
Month,  60. 
Morning  star,  31. 
Motion  in  line  of  sight,  89,  193. 
Multiple  stars,  202. 

Names  of  stars.  8. 
Nebulae,  214. 

density,  217. 

development  of,  245. 

motion,  218. 

spectra,  216. 

types  and  classes  of,  215. 
Nebular  hypothesis,  230. 

objections  to,  231. 
Neptune,  146. 

discovery  of,  41. 
Newton's  laws  of  motion,  34. 

law  of  gravitation,  37,  43. 
Nodes,  39. 

relation  to  eclipses,  67,  71. 
Nucleus,  of  comet,  160. 

Objective,  of  telescope,  78. 
Obliquity  of  ecliptic,  25. 
Observations,  of  stars,  10. 
Occultation  of  stars,  103. 
Orbits,  of  comets,  161. 

of  double  stars,  199. 

of  moon,  92. 


390 


ASTRONOMY 


Orbits,  of  planets,  38. 
Orion  nebula,  215. 

Parabola,  35,  38,  161. 
Parabolic  velocity,  38. 
Parallax,  114,  188. 
Penumbra,  64,  121. 
Perihelion,  38. 
Periodic  comets,  176. 
Personal  equation,  82. 
Perturbations,  39. 

of  meteors,  174. 
Phases,  of  the  moon,  91,  92. 
Photography,  81. 

of  stars,  13. 

Photosphere,  of  sun,  121. 
Planets,  26,  133. 

distances  from  the  sun,  134. 

how  to  find,  29. 

mass,  density,  size,  133. 

motion  of,  27,  38. 

periodic  times  of,  30. 
Planetary  nebulas,  215. 
Pleiades,  16,  215. 
Plumb-line  apparatus,  11,  18. 
Poles,  21. 
Precession,  46. 
Prisms,  84. 

Problem  of  three  bodies,  39. 
Prominences,  solar,  125. 
Proper  motions,  191. 
Protractor,  2. 
Ptolemaic  system,  32. 

Radiant  energy,  75. 

Radiant,  of  meteor  shower,  171. 

Radius  victor,  33. 

Reference  lines  and  circles,  17. 

Refraction,  50. 

Right  ascension,  16,  20,  21. 

Roche's  limit,  239. 

Rotation,  of  earth,  55. 


Rotation,  of  Mars,  151. 
of  moon,  99. 
of  Jupiter,  138. 
of  Saturn,  144. 
of  sun,  120,  132. 

Saros,  72. 

Satellites,  of  Jupiter,  136,  140. 

of  Mars,  155. 

of  Saturn,  145. 
Saturn,  142. 

ball  of,  144. 

orbit,  29. 

rings,  142. 

rotation,  144. 

satellites,  145. 
Seasons,  on  the  earth,  47. 

on  Mars,  151. 
Shadow  cone,  64,  66. 
Sidereal  time,  20,  54. 
Shooting  stars,  158.     (See  Meteor.) 
Spectroscope,  84. 
Spectroscopic  binaries,  203. 
Spectrum,  84,  87. 

of  comets,  182. 

of  nebulae,  216. 

of  stars,  211. 

types  of,  88. 
Spectrum  analysis,  85. 
Spiral  nebulae,  215. 
Standard  time,  57. 
Stars,  8,  184. 

classes  of,  212. 

clusters,  213. 

colors,  209. 

dark  stars,  201. 

development  of,  242. 

distances  from  the  sun,  188,  196. 

distribution  of,  220. 

double  stars,  198,  203. 

drift,  194. 

magnitudes,  9,  196. 


INDEX 


391 


Stars,  number  of,  185. 

spectra,  211. 

temporary,  208. 

variable,  204. 

Starlight,  absorption  of,  225. 
Star  maps,  construction  of,  23. 
Stellar  system,  extent  of,  223. 
Sun's  apparent  motion,  25. 

real  motion,  195. 
Sun,  110. 

chemical  composition,  116. 

chromosphere,  124. 

corona,  123. 

distance  from  the  earth,  111. 

f  acute,  119,  122. 

gaseous  constitution,  127. 

heat  of,  117. 

mechanism  of,  126. 

physical  properties,  115-120. 

prominences,  125. 

rotation,  120,  132. 

surface  of,  119. 

temperature,  118. 
Sun  spots,  119,  121. 

period,  129,  131. 

zones,  130. 

Telescopes,  78. 

equatorial  mounting  for,  80. 

magnifying  power  of,  79. 
Temperature  of  Jupiter,  139. 

of  Mars,  152. 

of  Mercury,  149. 

of  moon,  107. 

of  sun,  118. 
Temporary  stars,  208. 


Terminator,  91. 
Tenth  meter,  75. 
Tidal  friction,  233-238. 
Tides,  42. 
Time,  sidereal,  20,  54. 

solar,  52. 

determination  of,  20. 

equation  of,  53. 

standard,  57. 
Triangulation,  3. 
Trifid  nebula,  215. 
Twilight,  51. 
Twinkling,  of  stars,  48. 

Universe,  development  of,  226. 

stability  of,  247. 
Uranus,  146. 

Variable  stars,  204. 

Velocity,  its    relation    to    orbital 

motion,  38. 
Venus,  148. 

orbit  of,  30. 
Vernal  equinox,  21,  25. 
Vertical  circle,  21. 

Wave  front,  76. 
Wave  lengths,  75,  86. 

Year,  25. 
leap  year,  61. 
sidereal  year,  59. 
tropical  year,  60. 

Zenith,  21. 
Zodiac,  26. 
Zodiacal  light,  168. 


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